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All Textbook Solutions for Precalculus
In problems 3946, show that (fg)(x)=(gf)(x)=x. f(x)=9x6; g(x)=19(x+6)In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=43x ; g( x )=( 4x )In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=ax+b ; g(x)= 1 a (xb) a0In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f(x)= 1 x ; g(x)= 1 xIn Problems 47-52, find functions f and g so that fg=H . H(x)= (2x+3) 4In Problems 47-52, find functions f and g so that fg=H . H(x)= (1+ x 2 ) 3In Problems 47-52, find functions f and g so that fg=H . H(x)= x 2 +1In Problems 47-52, find functions f and g so that fg=H . H(x)= 1 x 2In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2x+1 |In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2 x 2 +3 |If f(x)=2 x 3 3 x 2 +4x1 and g(x)=2 , find (fg)( x ) and (gf)( x ) .If f(x)= x+1 x1 , find (ff)( x ) .If f(x)=2 x 2 +5 and g(x)=3x+a , find a so that the graph of fg crosses the y-axis at 23.If f(x)=3 x 2 7 and g( x )=2x+a , find a so that the graph of fg crosses the y-axis at 68.63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU1AYU2AYU3AYU4AYUIf x 1 and x 2 are two different inputs of a function f , then f is one-to-one if _____.If every horizontal line intersects the graph of a function f at no more than one point, then f is a(n) ______ function.If f is a one-to-one function and f( 3 )=8 , then f 1 ( 8 )= ________.If f 1 denotes the inverse of a function f , then the graphs of f and f 1 are symmetric with respect to the line _________.If the domain of a one-to-one function f is [ 4, ) , then the range of its inverse function f 1 is ________.True or False If f and g are inverse functions, then the domain of f is the same as the range of g .In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one.In Problems 13-20, determine whether the function is one-to-one. (2,6),(3,6),(4,9),(1,10)In Problems 13-20, determine whether the function is one-to-one. ( 2,5 ),( 1,3 ),( 3,7 ),( 4,12 )In Problems 13-20, determine whether the function is one-to-one. { ( 0,0 ),( 1,1 ),( 2,16 ),( 3,81 ) }In Problems 13-20, determine whether the function is one-to-one. { ( 1,2 ),( 2,8 ),( 3,18 ),( 4,32 ) }In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.In Problems 21-26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYUIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=3x+4 ; g(x)= 1 3 ( x4 )In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=32x ; g( x )= 1 2 ( x3 )In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=4x8 ; g( x )= x 4 +2In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )=2x+6 ; g( x )= 1 2 x3In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )= x 3 8 ; g(x)= x+8 3In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f( x )= (x2) 2 ; x2 ; g(x)= x +2In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= 1 x ; g(x)= 1 xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)=x ; g(x)=xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= 2x+3 x+4 ; g(x)= 4x3 2xIn Problems 35-44, verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f( x ))=x . Give any values of x that need to be excluded from the domain of f and the domain of g . f(x)= x5 2x+3 ; g(x)= 3x+5 12x43AYU44AYU45AYU46AYU47AYU48AYUIn Problems 51-62, the function f is one-to-one (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)=3xIn Problems 51-62, the function f is one-to-one (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)=4xIn Problems 51-62, the function f is one-to-one (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)=4x+2In Problems 51-62, the function f is one-to-one (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)=13xIn Problems 51-62, the function f is one-to-one (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f( x )= x 3 1In Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= x 3 +1In Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f( x )= x 2 +4,x0In Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= x 2 +9,x0In Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= 4 xIn Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= 3 xIn Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= 1 x2In Problems 51-62, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f , f 1 , and y=x on the same coordinate axes. f(x)= 4 x+2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2 3+xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 4 2xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x x+2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x x1In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x 3x1In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x+1 xIn Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x+4 2x3In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x3 x+4In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 2x+3 x+2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= 3x4 x2In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= x 2 4 2 x 2 , x0In Problems 63-74, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . f(x)= x 2 +3 3 x 2 x0Use the graph of to evaluate the following :
Use the graph of to evaluate the following :
If f( 7 )=13 and f is one-to-one, what is f 1 ( 13 ) ?If g( 5 )=3 and g is one-to-one, what is g 1 ( 3 ) ?The domain of a one-to-one function f is [ 5, ) , and its range is [ 2, ) . State the domain and the range of f 1 .The domain of a one-to-one function f is [0,) , and its range is [5,) . State the domain and the range of f 1 .The domain of a one-to-one function g is ( ,0 ] , and its range is [ 0, ) . State the domain and the range of g 1 .The domain of a one-to-one function g is [0,15] , and its range is (0,8) . State the domain and the range of g 1 .A function y=f( x ) is increasing on the interval [0,5] . What conclusions can you draw about the graph of y= f 1 (x) ?A function y=f( x ) is decreasing on the interval [0,5] . What conclusions can you draw about the graph of y= f 1 (x) ?Find the inverse of the linear function f( x )=mx+b,m0Find the inverse of the function f(x)= r 2 + x 2 , 0xrA function f has an inverse function f 1 . If the graph of f lies quadrant I, in which quadrant does the graph of f 1 lie?86AYU87AYUThe function f( x )= x 4 is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of the new function.In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y=f( x ) to represent a function, an applied problem might use C=C( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C=C( q ) will be q=q( C ) . So C=C( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q=q( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Vehicle Stopping Distance Taking into account reaction time, the distance d (in feet) that a car requires to come to a complete stop while traveling r miles per hour is given by the function d( r )=6.97r90.39 (a) Express the speed r at which the car is traveling as a function of the distance d required to come to a complete stop. (b) Verify that r=r( d ) is the inverse of d=d( r ) by showing that r( d( r ) )=r and d( r( d ) )=d . (c) Predict the speed that a car was traveling if the distance required to stop was 300 feet.In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y=f( x ) to represent a function, an applied problem might use C=C( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C=C( q ) will be q=q( C ) . So C=C( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q=q( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Height and Head Circumference The head circumference C of a child is related to the height H of the child (both in inches) through the function H( C )=2.15C10.53 (a) Express the head circumference C as a function of height H . (b) Verify that C=C( H ) is the inverse of H=H( C ) by showing that H( C( H ) )=H and C( H( C ) )=C . (c) Predict the head circumference of a child who is 26 inches tall.In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y=f( x ) to represent a function, an applied problem might use C=C( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C=C( q ) will be q=q( C ) . So C=C( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q=q( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W( h )=50+2.3( h60 ) (a) What is the ideal weight of a 6-foot male? (b) Express the height h as a function of weight W . (c) Verify that h=h( W ) is the inverse of W=W( h ) by showing that h( W( h ) )=h and W( h( W ) )=W . (d) What is the height of a male who is at his ideal weight of 80 kilograms? [Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given by W( h )=45.5+2.3( h60 ) .In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y=f( x ) to represent a function, an applied problem might use C=C( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C=C( q ) will be q=q( C ) . So C=C( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q=q( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Temperature Conversion The function F( C )= 9 5 C+32 converts a temperature from C degrees Celsius to F degrees Fahrenheit. (a) Express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F . (b) Verify that C=C( F ) is the inverse of F=F( C ) by showing that C( F( C ) )=C and F( C( F ) )=F . (c) What is the temperature in degrees Celsius if it is 70 degrees Fahrenheit?93AYU94AYUGravity on Earth If a rock falls from a height of 100 meters on Earth, the height H (in meters) after t seconds is approximately H( t )=1004.9 t 2 (a) In general, quadratic functions are not one-to-one. However, the function H is one-to-one. Why? (b) Find the inverse of H and verify your result. (c) How long will it take a rock to fall 80 meters?Period of a Pendulum The period T (in seconds) of a simple pendulum as a function of its length l (in feet) is given by T( l )=2 l 32.2 (a) Express the length l as a function of the period T . (b) How long is a pendulum whose period is 3 seconds?Given f( x )= ax+b cx+d f 1 ( x ) . If c0 , under what conditions on a , b , c , d is f= f 1 ?98AYU99AYU100AYU101AYU102AYU103AYU4 3 = ; 8 2/3 = ; 3 2 = . (pp. A8-A9 and pp, A89-A91)Solve: x 2 +3x=4 (pp. A47-A52)True or False To graph y= (x2) 3 , shift the graph of y= x 3 to the left 2 units. (pp. 106-114)4AYUTrue or False The function f(x)= 2x x3 has y=2 as a horizontal asymptote. (pp. 227-229)6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYUIn Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.30AYUIn Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 27-34, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.In Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn Problems 35-42, the graph of an exponential function is given. Match each graph to one of the following functions: (A) y =3 x (B) y =3 x (C) y= 3 x (D) y= 3 x (E) y =3 x 1 (F) y =3 x1 (G) y =3 1x (H) y=1 3 xIn problems 4556, use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function, f(x)=2x+1In problems 4556, use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function, f(x)=3x2In problems 4556, use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function, f(x)=3x1In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems 4556, use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function, f(x)=4(13)xIn problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In problems use the transformations to the graph each function. Determine the domain, range, horizontal asymptote and y-intercept of each function,
In Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f( x )= e xIn Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)= e xIn Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)= e x +2In Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)= e x 1In Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)=5 e xIn Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)=93 e xIn Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)=2 e x/2In Problems 55-62, begin with the graph of y= e x (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function. f(x)=73 e 2x61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYUIn Problems 89-92, determine the exponential function whose graph is given. 89.In Problems 89-92, determine the exponential function whose graph is given. 90.In Problems 89-92, determine the exponential function whose graph is given. 91.In Problems 89-92, determine the exponential function whose graph is given. 92.89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU105. Optics If a single pane of glass obliterates 3 of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function p(n)=100 ( 0.97 ) n (a) What percent of fight will pass through 10 panes? (b) What percent of light will pass through 25 panes? (c) Explain the meaning of the base 0.97 in this problem.102AYU107. Depreciation The price p, in dollars, of a Honda Civic EX-L sedan that is x years old is modeled by p( x )=22,265 ( 0.90 ) x (a) How much should a 3-year-old Civic EX-L sedan cost? (b) How much should a 9-year-old Civic EX-L sedan cost? (c) Explain the meaning of the base 0.90 in this problem.104AYU105AYU106AYU107AYU108AYU109AYU110AYU117. Relative Humidity The relative humidity is the ratio (expressed as a percent) of the amount of water vapor in the air to the maximum amount that the air can hold at a specific temperature. The relative humidity, R, is found using the following formula: R= 10 ( 4221 T+459.4 4231 D+459.4 +2 ) where T is the air temperature (in F ) and D is the dew point temperature (in F ). (a) Determine the relative humidity if the air temperature is 50 Fahrenheit and the dew point temperature is 41 Fahrenheit. (b) Determine the relative humidity if the air temperature is 68 Fahrenheit and the dew point temperature is 59 Fahrenheit. (c) What is the relative humidity if the air temperature and the dew point temperature arc the same?112AYU119. Current in an RL Circuit The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in voles) is I= E R [1 e (R/L)t ] (a) If E=120 volts, R=10 ohms, and L=5 henrys, how much current I1 is flowing after 0.3 second? After 0.5 second? After 1 second? (b) What is the maximum current? (c) Graph this function I= I 1 (t), measuring I along the y-axis and t along the x-axis . (d) If E=120 volts, R=5 ohms, and L=10 henrys, how much current I2 is flowing after 0.3 second? After 0.5 second? After 1 second? (e) What is the maximum current? (f) Graph the function I= I 2 ( t ) on the same coordinate axes as I 1 (t) .120. Current in an RC Circuit The equation governing the amount of current I (in amperes) after lime t (in microseconds) in a single RC circuit consisting of a resistance R (in ohms), a capacitance C (in microfarads), and an electromotive force E (in volts) is I= E R e t/ (RC) (a) If E=120 volts, R=2000 ohms, and C=1.0 microfarad, how much current I1 is flowing initially ( t=0 )? After 1000 microseconds? After 3000 microseconds? (b) What is the maximum current? (c) Graph this function I= I 1 (t), measuring I along the y-axis and t along the x-axis . (d) If E=120 volts, R=1000 ohms, and C=2.0 microfarads, how much current I2 is flowing initially? After 1000 microseconds? After 3000 microseconds? (e) What is the maximum current? (f) Graph the function I= I 2 ( t ) on the same coordinate axes as I 1 (t) .115AYU116AYU117AYU118AYU119AYU120AYU121AYU122AYU123AYU124AYU125AYU126AYU127AYU128AYU129AYUSolve each inequality: (a) 3x782x (pp.A79-A80) (b) x 2 x60 (pp.170-172)Solve the inequality: x1 x+4 0 (pp. 245-247)3AYU4AYU5AYU6AYU7AYUTrue or False The graph of f(x)=logax , where a0anda1 , has an x-intercept equal to 1 and no y-intercept .In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 9= 3 2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 16= 4 2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. a 2 =1.6In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. a 3 =2.1In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 2 x =7.2In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. 3 x =4.6In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. e x =8In Problems 11-18, change each exponential statement to an equivalent statement involving a logarithm. e 2. 2 =MIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 2 8=3In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 3 ( 1 9 )=2In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log a 3=6In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log b 4=2In Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 3 2=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. log 2 6=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. ln4=xIn Problems 19-26, change each logarithmic statement to an equivalent statement involving an exponent. lnx=4In Problems 27-38, find the exact value of each logarithm without using a calculator. log 2 1In Problems 27-38, find the exact value of each logarithm without using a calculator. log 8 8In Problems 27-38, find the exact value of each logarithm without using a calculator. log 5 25In Problems 27-38, find the exact value of each logarithm without using a calculator. log 3 ( 1 9 )In Problems 27-38, find the exact value of each logarithm without using a calculator. log 1/2 16In Problems 27-38, find the exact value of each logarithm without using a calculator. log 1/3 9In Problems 27-38, find the exact value of each logarithm without using a calculator. log 10 10In Problems 27-38, find the exact value of each logarithm without using a calculator. log 5 25 3In Problems 27-38, find the exact value of each logarithm without using a calculator. log 2 4In Problems 27-38, find the exact value of each logarithm without using a calculator. log 3 9In Problems 27-38, find the exact value of each logarithm without using a calculator. ln eIn Problems 27-38, find the exact value of each logarithm without using a calculator. ln e 3In Problems 39—50, find the domain of each function. f(x)=ln(x3)38AYUIn Problems 39—50, find the domain of each function. F(x)= log 2 x 2