2. Objectives
Add, subtract, multiply, and divide functions.

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) = f(x) + g(x)
= (4x2 + 3x – 1) + (6x + 2)
Substitute function rules.
= 4x2 + 9x + 1
Combine like terms.

5. Example 1B: Adding and Subtracting Functions
Given f(x) = 4x2 + 3x – 1 and g(x) = 6x + 2, find each function.
(f – g)(x)
(f – g)(x) = f(x) – g(x)
= (4x2 + 3x – 1) – (6x + 2)
Substitute function rules.
= 4x2 + 3x – 1 – 6x – 2
Distributive Property
= 4x2 – 3x – 3
Combine like terms.

6. Check It Out! Example 1a
Given f(x) = 5x – 6 and g(x) = x2 – 5x + 6, find each function.
(f + g)(x)
(f + g)(x) = f(x) + g(x)
= (5x – 6) + (x2 – 5x + 6)
Substitute function rules.
= x2
Combine like terms.

7. Check It Out! Example 1b
Given f(x) = 5x – 6 and g(x) = x2 – 5x + 6, find each function.
(f – g)(x)
(f – g)(x) = f(x) – g(x)
= (5x – 6) – (x2 – 5x + 6)
Substitute function rules.
= 5x – 6 – x2 + 5x – 6
Distributive Property
= –x2 + 10x – 12
Combine like terms.

8. When you divide functions, be sure to note any domain restrictions that may arise.

9. Example 2A: Multiplying and Dividing Functions
Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find each function.
(fg)(x)
(fg)(x) = f(x) ● g(x)
Substitute function rules.
= (6x2 – x – 12) (2x – 3)
= 6x2 (2x – 3) – x(2x – 3) – 12(2x – 3)
Distributive Property
= 12x3 – 18x2 – 2x2 + 3x – 24x + 36
Multiply.
= 12x3 – 20x2 – 21x + 36
Combine like terms.

10. (fg)(x) Given f(x) = x + 2 and g(x) = x2 – 4, find each function.
Check It Out! Example 2a
Given f(x) = x + 2 and g(x) = x2 – 4, find each function.
(fg)(x)
(fg)(x) = f(x) ● g(x)
= (x + 2)(x2 – 4)
Substitute function rules.
= x3 + 2x2 – 4x – 8
Multiply.