Activity 8.2 Inverse Functions
Overview:
This activity explores the concept of an inverse function.
Estimated Time Required:
This activity should take about 20 minutes.
Technology: None
Prerequisite Concepts:

Definition of a Function

Domain and range of a function

Which functions have inverses that are also functions
Discussion:
Review the definition of a function and the terms domain and range. Note that inverses undo
what the function does and that every function has an inverse, but that the inverse may or may
not be a function in its own right. Stress that a function has an inverse function if each output is
associated with only one input.
Illustrate the relationship between a function that is defined numerically and its inverse and then
give students the activity.
Activity 8.2 – Inverse Functions
Briefly describe the following:
 When does a function have an inverse?

How are the graphs of inverse functions related?

How are the domains and ranges of inverse functions related?

How do you find the inverse of a function algebraically?

How do you confirm that 2 functions are inverses of each other algebraically?
1. Is the function
f  x   x3  0.1x  1 invertible? Why or why not?
2. Given the function
f  t   t 5  t  1 , find f 1 100 .
3. Given the function
g  x   2x  x2 , find g 1  20  .
4. For each of the 3 functions below:
a.) Determine if the function is invertible. If not, restrict the domain to an interval on which it
is invertible.
b.) Find
f 1 algebraically.
c.) Graph both f and
f 1 on the same set of axes.
d.) State the domain and range of both f and
f  x   3 5x  2  7
3
f 1 (using the restrictions, if necessary).
f  x   3e5 x2  7
f  x   3sin  5x  2  7