1. Functions and Inverses

2. Inverses
An INVERSE RELATION “undoes” the relation. The Inverse of f(x) is denoted by f-1(x)

3. Inverse
So if f(x) = x – 5 Then f-1(x) = x + 5

4. Domains and Ranges
The domain of a relation’s inverse is its range, and the range of a relation’s inverse is its domain. f(x): D R f-1(x): D R -1 2 6 7 -1 2 6 7 1 2 4 1 2 4

5. More Inverse
Find the inverse of the following relation: {(2,3), (4,5), (1,3)}

6. Try some! Find the inverse of the following relations:
{(3,4), (-4, -6), (-3, 2), (6, -1)}
{(2, 5), (1, 5), (3, 5)}

7. Functionality of Inverses
If a relation is a function, does it’s inverse have to be??

8. How to find the inverse of a function:
Switch the x and y, and solve for y. Ex: y = 5x - 15

9. Find the inverse:
Ex: y = 6 – 2x

10. You Try! Find the Inverse of the following: y = x – 5 y = 2x + 10

11. Function Inverse Exit Ticket
Find the inverse of the following functions:
1. y = 3(x + 2) 2. y = 3x + 4x – 2
3. y = 2x y = 3x – 6
5. y = 6 – x 6. y = x
7. y = x y = -x + 3