1. Inverse Functions and Relations
Lesson 7.2
Inverse Functions and Relations

2. pg 2
Inverse Relations
Two relations are inverse relations if and only if one relation contains the element (a, b) the other relation contains the element (b, a)
Example: Q and S are inverse relations
Q = {(1, 2), (3, 4), (5, 6)}
S = {(2, 1), (4, 3), (6, 5)}

3. Examples 1. Find the inverse relation of {(2,1), (5,1), (2,-4)}
pg 2
Examples
1. Find the inverse relation of {(2,1), (5,1), (2,-4)}
2. Find the inverse relation of {(-8,-3), (-8,-6), (-3,-6)}

4. Property of Inverse Functions
pg 2
Property of Inverse Functions
Suppose f and f-1 are inverse functions. Then f(a) = b if and only if f -1 (b) = a
To find the inverse of a function:
1. Replace f(x) with y
2. Switch x and y
3. Solve for y
4. Replace y with f-1(x)
5. Graph f(x) and f-1(x) on the same coordinate plane

5. To Graph a function and it’s inverse
pg 2
To Graph a function and it’s inverse
1. Make an x/y chart for f(x) then graph the points and connect the dots
2. Make an x/y chart for f-1(x) by switching the x and y coordinates and then graph and connect the dots
- The graphs should be reflections of one another over the line y=x

6. Examples
3. Find the inverse of and then graph the function and its inverse
pg 3

7. pg 3
4. Find the inverse of and then graph the function and its inverse f(x) = 2x - 3

8. pg 3
Inverse Functions
Two functions f and g are inverse functions if and only if both of their compositions are the identity function.
[f o g](x) = x and [g o f](x) = x

9. 5. Determine if the functions are inverses
pg 3
5. Determine if the functions are inverses

10. 6. Determine if the functions are inverses
pg 3
6. Determine if the functions are inverses