1. Inverse Functions Consider a person walking, where time is calculated in seconds, and distance is calculated in feet.

2. In table form, the function might look like the following: Time 01234 Distance 010203040

3. Now consider another function related to the first.

4. In table form, the function g is given below: Distance 010203040 Time 01234

5. We say that function g is the inverse of function f.

6. Compare the Domain and Range of the two functions. f: Time 01234 Dist 010203040 g: Dist 010203040 Time 01234 Domain f Range f = Range g = Domain g

7. Notice the relationship of x -values and function values. f: Time 01234 Distance 010203040 g: Dist 010203040 Time 01234 f (3)=30 g (30)=3

8. Composite operation with inverses. f: Time 01234 Distance 010203040 g: Dist 010203040 Time 01234 f (g(30))=30=f(3)