1. Section 8.2 Inverse Functions

2. Consider the following two tables
Are they both functions?
What are f-1 and g-1? x
f(x) -2 10 -1 12 16 1 20 2 27 3 44 x
g(x) -5
-10 -2
-12 -1
-16 1 2 5

3. Definition of an Inverse Function
Suppose Q = f(t) is a function with the property that each value of Q determines exactly one value of t. The f has an inverse function, f -1 and
If a function has an inverse, it is said to be invertible

4. Graphs of Inverses
Consider the function

5. The inverse is

6. Plot of the two graphs together

8. A function is one-to-one if it passes the horizontal line test
A function must be one-to-one in order to have an inverse (that is a function)
A function is one-to-one if it passes the horizontal line test
A horizontal line may hit a graph in at most one point
We can restrict the domain of functions so their inverse exists
For example, if x ≥ 0, then we have an inverse for

9. Let’s talk about the following problems

10. Property of Inverse Functions
If y = f(x) is an invertible function and y = f -1(x) is its inverse, then

11. In your groups try problems 5, 15, and 25