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]

Fill in the Blank

The domain and range of a one-to-one function y=f(x), are given below in set builder notation. Give the domain of this function's inverse also in set-builder notation.

Domain: {x|-3 $\le$  x $<$  5}

Range: {y|y $>$  -2}

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

Fill in the Blank

Using the same function, A(r)= $\pi r^2$  , what are the values of  $A^{-1}\left(100\pi\right)$  and  $A^{-1}\left(225\pi\right)$  , respectively.

Separate your answers with a comma and no spaces. Put smaller answer first.

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

Fill in the Blank

A function's inverse is a function if and only if the original function is