1. Composite functions

2. Composite functions: A composition of functions combines functions so the output of one function becomes the input of the other.
If 𝑓 𝑥 =3 𝑥 2 +2, find each of the following:
𝑓 2
𝑓(−1)
𝑓 𝑚
𝑓 
𝑓(𝑥−1)

3. If 𝑓 𝑥 =2𝑥+1 and 𝑔 𝑥 =3𝑥, find each of the following: 1. 𝑓 𝑔 2 2

4. If p 𝑥 =5𝑥 and ℎ 𝑥 = 𝑥 2 +1, find each of the following: 1. ℎ 𝑝 𝑥 2

5. Notation:
𝑓 𝑔 𝑥 can be written as 𝑓∘𝑔 𝑥
𝑔(𝑓 𝑥 ) can be written as 𝑔∘𝑓 𝑥  

6. If 𝑓 𝑥 =𝑥+4 and 𝑔 𝑥 = 𝑥 2 , find each of the following: 1. 𝑓∘𝑔 𝑥 2

9. Inverse functions: A function and its inverse can be described as “DO” and “UNDO” functions. -all x and y values are switched -Notation: 𝑓 −1 Ex: y=3𝑥 and 𝑦= 𝑥 3 Recall: You can find the inverse of a function 3 ways 1. Numerically – from a table or set of ordered pairs. 2. Algebraically – from an equation 3. Graphically – from a picture

10. 1. Numerically: If 𝑓is a set of ordered pairs, ____________.
Find 𝑓 −1 if 𝑓 𝑥 = 0,1 , 2, −1 , −4,3

11. 1. Numerically: If 𝑓is a set of ordered pairs, ____________.
Find 𝑓 −1 if 𝑓 𝑥 = 0,1 , 2, −1 , −4,3

12. 2. Algebraically: If 𝑓 is written as a function, A. Solve for y B
2. Algebraically: If 𝑓 is written as a function, A. Solve for y B. Swap x and y C. Solve for y.
Find the inverse of 𝑓 𝑥 =𝑥−4
Find the inverse of 𝑓 𝑥 = 3 𝑥+4 2

13. 1. Graphically: Reflect the graph over the line y = x.
Find 𝑓 −1 if 𝑓 𝑥 = 0,1 , 2, −1 , −4,3