1. How do we verify and find inverses of functions?
Inverse Functions
M2 Unit 5a: Day 3
How do we verify and find inverses of functions?

2. Inverse functions: Two functions are inverses of one another if
The function g is denoted by , read as “f inverse.”
To verify two functions are inverses, use compositions

3. Watch me as I work one. Ex: Verify that functions are inverses
Verify that and are inverses.

4. You try:
Verify that f(x) and g(x) are inverse functions.

5. You try:
Verify that f(x) and g(x) are inverse functions.

6. You try:
Verify that f(x) and g(x) are inverse functions.

7. 4. Which pair of functions are inverses
4. Which pair of functions are inverses? (Use composition to determine the answer.)
a. b. c. d.

8. 5. Which pair of functions are inverses
5. Which pair of functions are inverses? (Use composition to determine the answer.)
a. b c. d.

9. Inverse Relations
An inverse relation maps the output values back to their original input values.
Basically, switch the domain and range of the relation to find the inverse.
Ex: Find the inverse.
Switch the x and y values x -2 -1 1 2 y 4 -4 x 4 2 -2 -4 y -1 1

10. Ex: 6 Now you try. Find the inverse of the relation. a) b) x 3 4 5 6 7-4 -2 2 x -4 -2 2 4 Y 3 5 6 7 x 1 3 6 9 12 y -1 -3 -6 -9
-12 x -1 -3 -6 -9
-12 y 1 3 6 9 12

11. Example 7: Watch me as I work one:
Find g(x), the inverse of the function.

12. Example 8: Find the inverse of a function
Consider the function Find the inverse.
Switch x and y and solve for y!

13. Example 9:
Find g(x), the inverse of the function.

14. Example 10: Find the inverse of the function:
Switch x and y and solve for y!
Is there any value that we can’t use for x?

15. 11. Which of the following is the inverse of ?
a. b c. d.

16. How do you read the symbol ?
In summary…
How do you read the symbol ?
“f inverse”
How do you verify that 2 functions are inverses of one another?
Use compositions to show that f(g(x)) = x and g(f(x)) = x.

17. Homework:
4.3 Practice Worksheet (#1-8, 12-17)