Inverse Functions

Inverse Functions

Multiple Choice

If the point (-7,5) lies on the graph of f(x) , which of the following points must lie on the graph of its inverse?

• (5,-7)

• (-1/7,1/5)

• (7,-5)

• (1/7,-1/5)

Multiple Choice

The function y=f(x) has an inverse function  $y=f^{-1}\left(x\right)$  . If f(a)=-b then which of the following must be true?

•  $f^{-1}\left(-b\right)=-a$  

•  $f^{-1}\left(\frac{1}{a}\right)=-\frac{1}{b}$  

•  $f^{-1}\left(-b\right)=a$  

•  $f^{-1}\left(b\right)=-a$  

Multiple Choice

The graph of the function y=g(x) is shown below. The value of

 $g^{-1}\left(2\right)$  is

• 2.5

• -4

• 0.4

• -1

Multiple Choice

Which of the following functions would have an inverse that is also a function?

Multiple Choice

For a one-to-one function it is known that f(0)=6 and f(8)=0. Which of the following must be true about the graph of this function's inverse?

• its y-intercept is 6

• its y-intercept is 8

• its x-intercept is -6

• its x-intercept is -8

Multiple Choice

If the domain of y=h(x) is [-5,4] and its range is [-4,1], what is the domain of  $y=h^{-1}\left(x\right)$  ?

• [4,-5]

• [5,-4]

• [-4,1]

• [4,-1]

Multiple Choice

The function y=A(r)= $\pi r^2$  is a one-to-one function that uses a circle's radius as an input and gives the circle's area as its output. What is the value of  $A^{-1}\left(9\pi\right)\$  and  $A^{-1}\left(36\pi\right)$  , respectively. 

• 81, 1296

• 81pi. 1296pi

• 3, 6

• 3pi, 6pi

Multiple Choice

The original function's input was the circle's radius and the output was the circle's area. What is the input and output of the inverse function?

• Input: circle's radius Output: circle's area

• Input: circle's area Output: circle's radius

• None of these