1. Ch. 7.6 Function Operations

2. Addition (f + g)(x) = f(x) + g(x) Multiplication
Function Operations
Addition
(f + g)(x) = f(x) + g(x)
Multiplication
(f * g)(x) = f(x) * g(x)
(f – g)(x) = f(x) – g (x)
Subtraction
Division

3. The domains of ƒ + g and ƒ – g are the set of real numbers.
Function Operations
ALGEBRA 2 LESSON 7-6
Let ƒ(x) = –2x + 6 and g(x) = 5x – 7. Find ƒ + g and ƒ – g and their domains.
(ƒ + g)(x) = ƒ(x) + g(x)
(ƒ – g)(x) = ƒ(x) – g(x)
= (–2x + 6) + (5x – 7)
= (–2x + 6) – (5x – 7)
= 3x – 1
= –7x + 13
The domains of ƒ + g and ƒ – g are the set of real numbers.
7-6

5. Let ƒ(x) = x2 + 1 and g(x) = x4 – 1. Find ƒ • g and and their domains.
Function Operations
ALGEBRA 2 LESSON 7-6 ƒ g
Let ƒ(x) = x2 + 1 and g(x) = x4 – 1. Find ƒ • g and and their domains. ƒ g
ƒ(x)
g(x)
(x) =
(ƒ • g)(x) = ƒ(x) • g(x)
x2 + 1
x4 – 1 =
= (x2 + 1)(x4 – 1) =
x2 + 1
(x2 + 1)(x2 – 1)
= x6 + x4 – x2 – 1 = 1
x2 – 1
The domains of ƒ and g are the set of real numbers, so the domain of ƒ • g is also the set of real numbers.
The domain of does not include 1 and –1 because g(1) and g(–1) = 0. ƒ g
7-6

6. p. 393 Check understanding # 2

7. Composition of Functions

8. Let ƒ(x) = x3 and g(x) = x2 + 7. Find (g ° ƒ)(2).
Function Operations
ALGEBRA 2 LESSON 7-6
Let ƒ(x) = x3 and g(x) = x Find (g ° ƒ)(2).
Method 1:
(g ° ƒ)(x) = g(ƒ(x)) = g(x3) = x6 + 7
Method 2:
(g ° ƒ)(x) = g(ƒ(x))
(g ° ƒ)(2) = (2)6 + 7 = = 71
g(ƒ(2)) = g(23)
= g(8) =
= 71
7-6

9. Check understanding p. 393 # 3

10. Homework
p. 394 # 2 – 42 even