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Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = /x +4. h(x) = (x + 4)* %3D f(x) =

Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = /x +4. h(x) = (x + 4)* %3D f(x) =

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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Question
Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \) and \( g(x) = \sqrt{x} + 4 \). \[ h(x) = \left( \sqrt{x} + 4 \right)^4 \] \[ f(x) = \Box \] In this problem, you need to find a function \( f(x) \) such that when it is composed with \( g(x) \), the result is the function \( h(x) \). Given \( g(x) = \sqrt{x} + 4 \), determine how \( f(x) \) transforms this expression to equal \( h(x) = \left( \sqrt{x} + 4 \right)^4 \).
Transcribed Image Text:Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \) and \( g(x) = \sqrt{x} + 4 \). \[ h(x) = \left( \sqrt{x} + 4 \right)^4 \] \[ f(x) = \Box \] In this problem, you need to find a function \( f(x) \) such that when it is composed with \( g(x) \), the result is the function \( h(x) \). Given \( g(x) = \sqrt{x} + 4 \), determine how \( f(x) \) transforms this expression to equal \( h(x) = \left( \sqrt{x} + 4 \right)^4 \).
Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \). Let \( g(x) = 3x + 7 \). \[ h(x) = \frac{9}{\sqrt{3x + 7}} \] \[ f(x) = \boxed{\phantom{x}} \]
Transcribed Image Text:Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \). Let \( g(x) = 3x + 7 \). \[ h(x) = \frac{9}{\sqrt{3x + 7}} \] \[ f(x) = \boxed{\phantom{x}} \]
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