College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter3: Functions
3.1 Functions And Function Notation 3.2 Domain And Range 3.3 Rates Of Change And Behavior Of Graphs 3.4 Composition Of Functions 3.5 Transformation Of Functions 3.6 Absolute Value Functions 3.7 Inverse Functions Chapter Questions Section3.7: Inverse Functions
Problem 1TI: Given that h1(6)=2 , what are the corresponding input and output values of the original function h? Problem 2TI: If f(x)=x34 and g(x)=x43 , is g=f1? Problem 3TI: If f(x)=(x1)3 and g(x)=x3+1 , is g=f1 ? Problem 4TI: The domain of function f is (1,) and the range of function f is (,2)Find the domain and range of the... Problem 5TI: Using Table 4, find and interpret a. f(60) , and b. f1(60) . Problem 6TI: Using the graph in Figure 6, a. find g1(1) , and b. estimate g1(4) . Problem 7TI: Solve for x in terms of y given y=13(x5) Problem 8TI: What is the inverse of the function f(x)=2x ? State the domains of both the function and the inverse... Problem 9TI: Draw graphs of the functions fandf1 from Example 8. Problem 1SE: Describe why the horizontal line test is an effective way to determine whether a function is... Problem 2SE: Why do we restrict the domain of the function f(x)=x2 to find the function's inverse? Problem 3SE: Can a function be its own inverse? Explain. Problem 4SE: Are one-to-one functions either always increasing or always decreasing? Why or why not? Problem 5SE: How do you find the inverse of a function algebraically? Problem 6SE: Show that the function fx)=ax is its own inverse for all real numbers a. Problem 7SE: For the following exercises, find f1(x) for each function. 7. f(x)=x+3 Problem 8SE: For the following exercises, find f1(x) for each function. 8. f(x)=x+5 Problem 9SE: For the following exercises, find f1(x) for each function. 9. f(x)=2x Problem 10SE: For the following exercises, find f1(x) for each function. 10. f(x)=3x Problem 11SE: For the following exercises, find f1(x) for each function 11. f(x)=xx+2 Problem 12SE: For the following exercises, find f1(x) for each function. 12. f(x)=2x+35x+4 Problem 13SE: For the following exercises, find a domain on which each function f is one-to-one and... Problem 14SE: For the following exercises, find a domain on which each function f is one-to-one and... Problem 15SE: For the following exercises, find a domain on which each function f is one-to-one and... Problem 16SE: For the following exercises, find a domain on which each functionfis one-to-one and non-decreasing.... Problem 17SE: For the following exercises, use function composition to verify that f(x) and g(x) are inverse... Problem 18SE: For the following exercises, use function composition to verify that f(x) and g(x) are inverse... Problem 19SE: For the following exercises, use a graphing utility to determine whether each function is one-to-one... Problem 20SE: For the following exercises, use a graphing utility to determine whether each function is one-to-one... Problem 21SE: For the following exercises, use a graphing utility to determine whether each function is one-to-one... Problem 22SE: For the following exercises, use a graphing utility to determine whether each function is one-to-one... Problem 23SE: For the following exercises, determine whether the graph represents a one-to-one function Problem 24SE: For the following exercises, determine whether the graph represents a one-to-one function Problem 25SE: For the following exercises, use the graph of f shown in Figure 11. Find f(0). Problem 26SE: For the following exercises, use the graph offshown in Figure 11. 26. Solve f(x)=0 . Problem 27SE: For the following exercises, use the graph of f shown in Figure 11. 27. Find f1(0) . Problem 28SE: For the following exercises, use the graph of f shown in Figure 11. 28. Solve f1(x)=0 . Problem 29SE: For the following exercises, use the graph of the one-to-one function shown in Figure 12. 29. Sketch... Problem 30SE: For the following exercises, use the graph of the one-to-one function shown in Figure 12. 30. Find... Problem 31SE: For the following exercises, use the graph of the one-to-one function shown in Figure 12. If the... Problem 32SE: For the following exercises, use the graph of the one-to-one function shown in Figure 12. If the... Problem 33SE: For the following exercises, evaluate or solve, assuming that the functionfis one-to-one. 33. If... Problem 34SE: For the following exercises, evaluate or solve, assuming that the functionfis one-to-one. 34. If... Problem 35SE: For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If... Problem 36SE: For the following exercises, evaluate or solve, assuming that the function f is one-to-one. If... Problem 37SE: For the following exercises, use the values listed in Table 6 to evaluate or solve. 37.Find f(1) . Problem 38SE: For the following exercises, use the values listed in Table 6 to evaluate or solve. 38. Solve f(x)=3... Problem 39SE: For the following exercises, use the values listed in Table 6 to evaluate or solve. 39.Find f1(0) . Problem 40SE: For the following exercises, use the values listed in Table 6 to evaluate or solve. 40. Solve... Problem 41SE: Use the tabular representation of f in Table 7 to create a table for f1(x) . Problem 42SE: For the following exercises, find the inverse function. Then, graph the function and its inverse... Problem 43SE: For the following exercises, find the inverse function. Then, graph the function and its inverse... Problem 44SE: For the following exercises, find the inverse function. Then, graph the function and its inverse... Problem 45SE: To convert from x degrees Celsius toy degrees Fahrenheit, we use the formula f(x)=95x+32 . Find the... Problem 46SE: The circumference C of a circle is a function of its radius given by C(r)=2r. Express the radius of... Problem 47SE: A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a... Problem 46SE: The circumference C of a circle is a function of its radius given by C(r)=2r. Express the radius of...
Related questions
Find the area of a regular hexagon inscribed in a circle of radius 1. How close is this area to that of the circle? (a) Find the area An of an n-sided regular polygon inscribed in a circle of radius 1. Write your answer as a function of n. (b) Complete the table. What number does An approach as n gets larger and larger?
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Definition Definition Two-dimentional plane figure composed of a finite number of straight line segments connected to form a closed chain or circuit. A polygonal circuit's segments are known as its edges or sides, and the points where two edges meet are known as its vertices or corners.
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