1. Chapter 6: Radical functions and rational exponents
Section 6.7: Inverse Relations and functions

2. Section 6.7: Inverse relations and functions
Goal: To find the inverse of a relation or function

3. Section 6.7: Inverse relations and functions
Inverse Relation: obtained by interchanging the first and second coordinates in every pair of the original relation
i.e. the domain for the inverse is the range for the original…the range for the inverse is the domain for the original

4. Section 6.7: Inverse relations and functions
Example
1. Find the inverse of the function {(1, 1), (1.5, 1), (2, 2), (2.5, 2)}. State the domain and range of this inverse. Determine if the inverse is a function.

5. Section 6.7: Inverse relations and functions
Inverse function: if f is the function, then its inverse is denoted by f-1
One-to-one correspondence: when both the original and the inverse are functions
To find the inverse function, switch the x and y variables

6. Section 6.7: Inverse relations and functions
Examples:
2. Find the inverse of the function
and determine if the inverse is also a function. Graph f, f-1, and y = x on the same coordinate plane.

7. Section 6.7: Inverse relations and functions
Examples:
What is f-1 if f(x) = Find f-1(7)

8. Section 6.7: Inverse relations and functions
Examples:
If f(x) = 8x + 1, what is f(f-1(4)) and f-1(f(-3))
What is f-1(f(x)) and f(f-1(x))

9. Section 6.7: Inverse relations and functions
Examples
Give five points on f-1(x) if f(x) = -2x2 – 3
What is f-1(-13) if f(x) = -6x + 11

10. Section 6.7: Inverse relations and functions
Examples:
What is the domain and range of f-1(x) if
f(x)= -4|9+5x| + 3

11. Section 6.7: Inverse relations and functions
Graph the inverse for the following graph
(-6, 3)
(5, 2)
(0, 0)
(-2, -1)

12. Section 6.7: Inverse relations and functions
Homework: Pg. 410 #8-40 (even)