MTH04 (Online)

Inverse Functions (Section 11.2) – Practice Problems

 

Created by: Joe Joyner

 

  1. If   , find  .

 

  1. Determine whether the inverse of   is also a function.  Explain how you arrived at your conclusion.

 

  1. Which of the following is the graph of the inverse of   ?

 

A.                    B. 

 

 

 

C.                     D.  

 

 

 

  1. Graph the inverse of the function  .

 

 

 

  1. If   ,  find  .

 

A.  122                        B.  -116           C.  2                D.  0.008

 

  1. If   , find  .

 

 

  1. Given that  and its inverse   ,

 

a.          find the point P where the line segment between  and  crosses  the graph of  .

b.         find the distance from   to  P  and the distance from    to  P.

c.          find the slope of the line segment between   and   .

d.         Do your results support the relationships that must be true for the graph of a function and its inverse?

 

 

Answer Key

 

 

1.     

 

2.      No, the inverse of  is not a function because  the graph of  does not pass the horizontal line test.

 

(Alternative answer):  No, the inverse of  is not a function because  is not one-to one on its domain.

 

3.      B

 

4.      Graph of   :

 

 

 

 

Graph of : 

 

 

 

Graph of    ,  and  :  

 

5.      C

 

6.       

 

7.       

a. 

 

b.    ,  

 

c.  m = -1

 

d.  (various answers)