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Find two functions fand g such that h(x) = (fog)(x) and f(x) + g(x) + x. h(x)=(x-3)² ƒ(x) = ¯ and g(x)= X

Find two functions fand g such that h(x) = (fog)(x) and f(x) + g(x) + x. h(x)=(x-3)² ƒ(x) = ¯ and g(x)= 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
## Problem Description Find two functions \( f \) and \( g \) such that \( h(x) = (f \circ g)(x) \) and \( f(x) \neq g(x) \neq x \). Given function: \[ h(x) = (x - 3)^2 \] ### Input Fields - \( f(x) = \) [Input Box] - \( g(x) = \) [Input Box] ### Diagram/Icons Explanation - A composite function diagram is shown, symbolized by two overlapping squares, representing the composition \( (f \circ g) \). - An "X" button and a reset button are available for clearing inputs or restarting the problem. ### Instructions To solve this problem: 1. Identify the function \( g(x) \) that when plugged into \( f(x) \) results in the given \( h(x) = (x - 3)^2 \). 2. Ensure that neither \( f(x) \) nor \( g(x) \) are equal to \( x \), and that they are distinct from each other. ### Example Solutions For instance, if \( g(x) = x - 3 \), then \( f(x) = x^2 \) will satisfy the given equation because: \[ (f \circ g)(x) = f(g(x)) = f(x - 3) = (x - 3)^2 \] Therefore, the two functions could be: - \( f(x) = x^2 \) - \( g(x) = x - 3 \) You can input these functions respectively into the provided input boxes and verify there are no other constraints.
Transcribed Image Text:## Problem Description Find two functions \( f \) and \( g \) such that \( h(x) = (f \circ g)(x) \) and \( f(x) \neq g(x) \neq x \). Given function: \[ h(x) = (x - 3)^2 \] ### Input Fields - \( f(x) = \) [Input Box] - \( g(x) = \) [Input Box] ### Diagram/Icons Explanation - A composite function diagram is shown, symbolized by two overlapping squares, representing the composition \( (f \circ g) \). - An "X" button and a reset button are available for clearing inputs or restarting the problem. ### Instructions To solve this problem: 1. Identify the function \( g(x) \) that when plugged into \( f(x) \) results in the given \( h(x) = (x - 3)^2 \). 2. Ensure that neither \( f(x) \) nor \( g(x) \) are equal to \( x \), and that they are distinct from each other. ### Example Solutions For instance, if \( g(x) = x - 3 \), then \( f(x) = x^2 \) will satisfy the given equation because: \[ (f \circ g)(x) = f(g(x)) = f(x - 3) = (x - 3)^2 \] Therefore, the two functions could be: - \( f(x) = x^2 \) - \( g(x) = x - 3 \) You can input these functions respectively into the provided input boxes and verify there are no other constraints.
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