Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = /x +5. h(x) = (Vx +5)* f(x)=

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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Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \) and \( g(x) = \sqrt{x} + 5 \).

\[ h(x) = \left( \sqrt{x} + 5 \right)^4 \]

\[ f(x) = \, \]

The task is to determine the function \( f(x) \) such that when it is composed with \( g(x) \), the result is \( h(x) \). Here, \( g(x) = \sqrt{x} + 5 \), and \( h(x) \) is given by the expression \(\left( \sqrt{x} + 5 \right)^4 \). You are required to fill in the expression for \( f(x) \) in the space provided. 

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Transcribed Image Text:Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \) and \( g(x) = \sqrt{x} + 5 \). \[ h(x) = \left( \sqrt{x} + 5 \right)^4 \] \[ f(x) = \, \] The task is to determine the function \( f(x) \) such that when it is composed with \( g(x) \), the result is \( h(x) \). Here, \( g(x) = \sqrt{x} + 5 \), and \( h(x) \) is given by the expression \(\left( \sqrt{x} + 5 \right)^4 \). You are required to fill in the expression for \( f(x) \) in the space provided. Helpful links for support: - Help me solve this - View an example - Get more help
Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \). Let \( g(x) = 2x + 6 \).

\[
h(x) = \frac{2}{\sqrt{2x + 6}}
\]

\[ 
f(x) = \boxed{\phantom{x}}
\]
Transcribed Image Text:Find \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \). Let \( g(x) = 2x + 6 \). \[ h(x) = \frac{2}{\sqrt{2x + 6}} \] \[ f(x) = \boxed{\phantom{x}} \]
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