1. Pre-Calculus - Section 4.5 INVERSE FUNCTIONS

2. WARM-UP

3.  When is f a function?  When each input goes to exactly 1 output  Determine if the following are functions REVIEW: FUNCTIONS xy 16 26 36 46 56 xy 12 23 34 45 216

4.  Inverse functions “undo” each other. WHAT IS AN INVERSE REALLY? DomainRange Function RangeDomain Inverse

5. WE USES THE CONCEPT OF INVERSE FUNCTIONS ALL OF THE TIME. For example, someone give us directions to their house. Turn right, go three blocks, turn left, go one block, and turn left again. We would use the inverse to go home. Come up with another example of inverse functions in every day life.

6. HOW TO FIND AN INVERSE GIVEN POINTS x f(x) 1245912459 3 6 12 15 27 xf -1 (x) 1245912459 3 6 12 15 27

7. EXAMPLE 1

8.  Horizontal Line Test:  If one output from the original function goes to multiple inputs, then what will happen when with the inverse?  Determine if the inverse will be a function: WHEN IS THE INVERSE A FUNCTION?

9. HOW TO CREATE AN INVERSE

10. EXAMPLE 2

11. YOU TRY. Find the inverse function:

12. EXAMPLE 3

13.  Functions f and g are inverse if g(f(x)) = x and f(g(x)) = x for all x in either domain. COMPOSITION

14. EXAMPLE 3

15.  Textbook: p.149 #7-15, 20 ***rule = equation of the inverse HOMEWORK