1. Inverse Functions
Rita Korsunsky

2. Definition x
f(x) b
f(b) a
f(a) R D
Definition

3. Horizontal Line Test
If the graph of a function y = f(x) is such that no horizontal line intersects the graph in more than one point ,then it is one to one and has an inverse function.
One-to-one function.
Has an inverse function
Not one-to-one.
Has no inverse function

4. Definitions Example 1 f(x) and g(x) are inverse functions if :
1)  g(f(x)) = x for all x in the domain of f
2)  f(g(x)) = x for all x in the domain of g  
Example 1

5. For every point (a,b) on the graph of f
the point (b,a) is on the the graph of f-1
The graph of f-1 is the reflection of graph of f
in line y= x

6. Example 2

7. Example 3

8. Guidelines for finding ƒ-1

9. Theorems

10. prove:
Derivatives of Inverse functions (slopes of tangents) are reciprocals of each other at the points where domain x and range y are interchanged(scroll down to see slopes calculated)

11. Example

12. Example (when g(2) is not given)

13. Another proof(optional)