1. Warm Up #8 Sketch the graphs of: 1. 𝑓 𝑥 = 𝑥+2 2 −2 2. 𝑓 𝑥 = 𝑥−5 +3
1. 𝑓 𝑥 = 𝑥+2 2 −2
2. 𝑓 𝑥 = 𝑥−5 +3
𝑓 𝑥 = 𝑥 3 𝑔 𝑥 = 1 𝑥
3. Find 𝑓∘𝑔
4. Find 𝑔∘𝑓
5. Find 𝑓∘𝑓

2. Warm Up # 9
Find the domain: 1. 𝑓 𝑥 = 𝑥+1 2. 𝑓 𝑥 = 2 𝑥 2 −2𝑥 Simplify: 3. 7−10 7−𝑥 𝑥 3 2 −2 +4 Solve for x in terms of y: 5. 𝑦= 3 2𝑥−4

3. 1-6:
Inverse Functions

4. Objectives You will be able to: Find the inverse of a function
Graph the inverse of a function

5. Inverse Function
An inverse function is when the domain and range switch, denoted by 𝑓 −1 𝑥 Ex. 𝑓 𝑥 = 1,5 , 2,6 , 3,7 , (4,8) 𝑓 −1 𝑥 = 5,1 , 6,2 , 7,3 , (8,4)

6. How to find the inverse of a function
Replace 𝑓 x with y.
Switch the x and the y.
Solve for y.
Replace y with 𝑓 −1 (x)

7. Example 1:
Find the inverse of 𝑓 𝑥 =𝑥+2

8. Example 2:
Find the inverse of 𝑓 𝑥 = 𝑥 3 −1

9. Not all functions have inverses
A function has an inverse if it passes a horizontal line test
Has an inverse
Does not Have an inverse

10. Example 3:
Does this function have an inverse?

11. Example 4:
Sketch the graph of the inverse functions: 𝑓 𝑥 = 𝑥 2 , 𝑥≥0 𝑎𝑛𝑑 𝑓 −1 𝑥 = 𝑥

12. Example 5:
Show that the functions are inverses (𝑓∘𝑔 𝑥 =𝑥 𝑎𝑛𝑑 𝑔∘𝑓 𝑥 =𝑥). 𝑓 𝑥 =2 𝑥 3 −1 𝑎𝑛𝑑 𝑔 𝑥 = 3 𝑥+1 2

13. Summary In this lesson we learned to: Find the inverse of a function
Graph the inverse of a function

14. Warm Up # 12
1. Find the equation of the line that is horizontal, going through point (1,2)
2. Find f(6) when f(x) = 3x+5
3. Find the domain of 5 𝑥+1
4. X varies directly with the square of y and inversely with z. Write a general formula when x=16 y=4 and z=2