Ch. 7.6 Function Operations

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

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

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

p. 393 Check understanding # 2

Composition of Functions

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) = x2 + 7. 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 = 64 + 7 = 71 g(ƒ(2)) = g(23) = g(8) = 82 + 7 = 71 7-6

Check understanding p. 393 # 3

Homework p. 394 # 2 – 42 even