1. Let int r + 2 f(x) = int x – 2 where int r is the greatest integer function. (a) Find the domain of f. (b) Is ƒ injective? 2. If two functions f and g have inverses, then (f og)-1 = g-1 of-!. Let f(r) = 2x – 1 and g(x) = 3x + 4. Find the following: (a) f-'(x) (b) g-'(x) (c) (f o g)-'(x) (d) (go f)-'(x) (e) (f-1 og¬1) (x) 3. Does every odd function have an inverse? Give a counterexample. (A counterexample is an example that disproves a statement. For example, to disprove the statement “every whole number is even", a counterexample would be 3.) 4. Find a quadratic function of the form f(x) = ax² + bx + c that satisfies the following conditions. The graph of f passes through the point (1,5) and has vertex (-3, –2).

Q: Consider the function ?(?) =1/x and the data points ( 0.1, 10), (0.2, 5), (0.3,3.33) Find Lagrange…

A: Introduction: The formula of Lagrange interpolation polynomial is given by,…

Q: 11. (a) State the largest possible domain of the following functions: opk fix → x-3 x+2 h:xx²+3…

A:

Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: If f(z) <0 for all real numbers z then f is decreasing on (-o, 00) Select one: O a. False O b. True

A:

Q: How do you show the inverse image of the intersecction of S and T equals the intersection of the…

A: To prove : f-1(S∩T)=f-1(S)∩f-1(T) To show f-1(S∩T)=f-1(S)∩f-1(T) need to prove…

Q: Find the criticial numbers for f(x) = xlnx

A: Given, The function is f(x) = x lnx

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: '(x) = ( 13 + x1, (x-1)², x x

A: T(x)=|3+x|x&lt;-1(x-1)2x≥-1

Q: Find the open intervals on which the function f(x)=x+6*sqrt(5−x) is increasing or decreasing.

A: Given, f(x)=x+65-x

Q: Find the absolute extrema of the following function on the indicated interval.  f(x)=x^3+2x^2-3x+4…

A:

Q: 3) f = {(0, a), (1, d), (5, e), (9, c)} find the inverse of this function.

A:

Q: уто ņx=-5 O SONGS & + 10 9 7 6 5 4 012345 -10-9-8-7 -6 -5 -4 -3 -2 -10 -2 -4 1) lim f(x) = x-(-4)…

A: Sol:- We have to explain what is telling by limits and the points for which f(x) is not…

Q: Suppose a car drives north on I-95 starting from Miami. Let f(t) denote thenumber of miles from…

A: f(5) − f(3)/5 − 3 represent displacemennt/time taken from 3hours to 5 hours i.e. 2 hours

Q: Let X=[-1,1] and Y=[0,1], and define the function f:X-->Y by f(x)=x^2. Which of the following is NOT…

A:

Q: Based on the definition of divided difference, show that f[x1,x2,x3] = f[x2,x1,x3

A:

Q: Consider the possible functions from [7] to [9].  How many in which f-1 is not a functio

A: Let f:7→9 is a function then, Let A=[7] and B=[9] So, n(A)=7 and n(B)=9 Now, the total functions of…

Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

Q: Let f(x) = −3x² + 1 1 X3 + −xª. Find all local and absolute maxima and minima of f.

A:

Q: what should n be if f(x) = Xn defineof a polynomial function?

A:

Q: J 3(x)is even function 0 صواب ihi O

A: We will use the fact that j_-n(x) =(-1)^n j_n(x) to decide whether j_3(x) is even or odd function.

Q: For the function f(x) = 3* find fx-2)

A: Given that: f(x)=3x.   NOTE: As per our answering guidelines, we can only answer 1 question or 3…

Q: How do you show the image of the union of S and T is equal to the union of the image of S and the…

A:

Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…