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9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that Q(x) = f(g(h(x))). Which functions f, g, and h below are correct? OB. h(x)=4x-5 O A. h(x)=4x- 5 g(x) = cos(x) f(x)=x² g(x) = x f(x) = cos(x)-5 OC. h(x) = cos(x)-5 OD. h(x) = 4x g(x)=x g(x) = cos(x)-5 9 f(x) = 4x f(x)=x OE. h(x) = 4x-5 OF. h(x) = cos (x) g(x)=x g(x)=x f(x) = cos(x) f(x) = 4x-5

9 To express Q(x) = cos(4x-5) as the composition of three functions, identify f, g, and h so that Q(x) = f(g(h(x))). Which functions f, g, and h below are correct? OB. h(x)=4x-5 O A. h(x)=4x- 5 g(x) = cos(x) f(x)=x² g(x) = x f(x) = cos(x)-5 OC. h(x) = cos(x)-5 OD. h(x) = 4x g(x)=x g(x) = cos(x)-5 9 f(x) = 4x f(x)=x OE. h(x) = 4x-5 OF. h(x) = cos (x) g(x)=x g(x)=x f(x) = cos(x) f(x) = 4x-5

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Understanding Function Composition To express \( Q(x) = \cos^9 (4x - 5) \) as the composition of three functions, we need to determine the functions \( f \), \( g \), and \( h \) such that \( Q(x) = f(g(h(x))) \). --- #### Problem Statement Which functions \( f \), \( g \), and \( h \) below are correct? --- #### Options - **A.** - \( h(x) = 4x - 5 \) - \( g(x) = \cos (x) \) - \( f(x) = x^9 \) - **B.** - \( h(x) = 4x - 5 \) - \( g(x) = x^9 \) - \( f(x) = \cos (x) \) - **C.** - \( h(x) = \cos (x) - 5 \) - \( g(x) = x^9 \) - \( f(x) = 4x \) - **D.** - \( h(x) = 4x \) - \( g(x) = \cos (x) - 5 \) - \( f(x) = x^9 \) - **E.** - \( h(x) = 4x - 5 \) - \( g(x) = x \) - \( f(x) = \cos (x) \) - **F.** - \( h(x) = \cos (x) \) - \( g(x) = x^9 \) - \( f(x) = 4x - 5 \) --- #### Explanation To find the correct option, let's break down \( Q(x) = \cos^9 (4x - 5) \) into three functions: 1. First, let’s define \( h(x) = 4x - 5 \). 2. Then, define \( g(x) = \cos (x) \). 3. Finally, define \( f(x) = x^9 \). So, \( Q(x) = f(g(h(x))) \). 1. \( h(x) = 4x - 5 \) 2. \( g(x) = \cos (x) \) 3. \(
Transcribed Image Text:### Understanding Function Composition To express \( Q(x) = \cos^9 (4x - 5) \) as the composition of three functions, we need to determine the functions \( f \), \( g \), and \( h \) such that \( Q(x) = f(g(h(x))) \). --- #### Problem Statement Which functions \( f \), \( g \), and \( h \) below are correct? --- #### Options - **A.** - \( h(x) = 4x - 5 \) - \( g(x) = \cos (x) \) - \( f(x) = x^9 \) - **B.** - \( h(x) = 4x - 5 \) - \( g(x) = x^9 \) - \( f(x) = \cos (x) \) - **C.** - \( h(x) = \cos (x) - 5 \) - \( g(x) = x^9 \) - \( f(x) = 4x \) - **D.** - \( h(x) = 4x \) - \( g(x) = \cos (x) - 5 \) - \( f(x) = x^9 \) - **E.** - \( h(x) = 4x - 5 \) - \( g(x) = x \) - \( f(x) = \cos (x) \) - **F.** - \( h(x) = \cos (x) \) - \( g(x) = x^9 \) - \( f(x) = 4x - 5 \) --- #### Explanation To find the correct option, let's break down \( Q(x) = \cos^9 (4x - 5) \) into three functions: 1. First, let’s define \( h(x) = 4x - 5 \). 2. Then, define \( g(x) = \cos (x) \). 3. Finally, define \( f(x) = x^9 \). So, \( Q(x) = f(g(h(x))) \). 1. \( h(x) = 4x - 5 \) 2. \( g(x) = \cos (x) \) 3. \(
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