5. Verifying Inverse Functions by Composition

Explanation

To verify inverses, compose the function with its inverse.

If:
f(f⁻¹(x)) = x
and
f⁻¹(f(x)) = x

Then they are inverses.

Simple idea:

• Do a function

• Undo it

• You end up where you started

Example:
f(x) = x + 2
f⁻¹(x) = x − 2

f(f⁻¹(x)) = (x − 2) + 2 = x

Quiz: Verifying Inverse Functions

1. What does it mean to verify inverses?

2. What should the result be when composing inverses?

3. If f(x) = x + 3, what is f⁻¹(x)?

4. What does f(f⁻¹(x)) equal?

5. True or False: If the result is x, the functions are inverses.

Answer Key

1. Checking if functions undo each other

2. x

3. x − 3

4. x

5. True