1. Do Now: Given: Express z in terms of x HW: p.159 # 4,6,8,
Aim: What is the composition of functions?
Do Now:
Given:
Express z in terms of x
HW: p.159 # 4,6,8,
p.159 # 14,15,16 (part a only) p.160 # 26

2. The notation is the symbol ○ is read “of ”.
Let and g(x) = x + 1
We can apply one function into another function.
This process is called composition of functions
The notation is the symbol ○ is read “of ”.
When we evaluate composition of functions, we go from inside to outside.
f(g(x)) =

3. How do we compose f(x) = 2x + 3 and g(x) = x – 1?
g is the inside function and f is the outside function. When you compute the composition, you compute the inside function first and then plug that result into the outside function.

4. Examples
Let
Then
Notice that g is the inside function and f is the outside function.

5. First of all, we evaluate g(2) = 2(2) = 4
If f(x) = 3x – 1 and g(x) = 2x, evaluate
First of all, we evaluate g(2) = 2(2) = 4
Then we evaluate f(4) = 3(4) – 1 = 12 – 1 = 11
If f(x) = 4x, g(x) = 3x + 1, evaluate f(g(-1))
g(–1) = 3(–1) + 1 = – = – 2
f(–2) = 4(–2) = –8

6. Examples
Let
Evaluate: a. f(g(x)) b. g(f(x))

7. Example If
Evaluate 3. 4.