1. Simplify. Assume that all expressions are defined.
Warm Up
Simplify. Assume that all expressions are defined.
1. (2x + 5) – (x2 + 3x – 2)
2. (x – 3)(x + 1)2 3.

2. Objectives Vocabulary Add, subtract, multiply, and divide functions.
Write and evaluate composite functions.
Vocabulary
composition of functions

3. You can perform operations on functions in much the same way that you perform operations on numbers or expressions. You can add, subtract, multiply, or divide functions by operating on their rules.

4. Example 1A: Adding and Subtracting Functions
Given f(x) = 4x2 + 3x – 1 and g(x) = 6x + 2, find each function.
(f + g)(x)
(f – g)(x)

5. Example 2A: Multiplying and Dividing Functions
When you divide functions, be sure to note any domain restrictions that may arise.
Example 2A: Multiplying and Dividing Functions
Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find each function.
( )
(x) f g
(fg)(x)

6. The composition (f o g)(x) or f(g(x)) is read “f of g of x.”
Reading Math

7. Example 3A: Evaluating Composite Functions
Given f(x) = 2x and g(x) = 7 – x, find each value.
f(g(4))
g(f(4))

8. Example 4A: Writing Composite Functions
Given f(x) = x2 – 1 and g(x) = ,
write and simplify each composite function. State the domain of each. x
1 – x

9. Given the following functions, write and simplify the composite function. State the domain of each.
Homework Pg , 45-48, Accel add 39-42