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f(x) g(x) | 2 (f °g)(x) (g • f)(x) 1 5 3 3 4 1 4 2 5 1 4 N3

f(x) g(x) | 2 (f °g)(x) (g • f)(x) 1 5 3 3 4 1 4 2 5 1 4 N3

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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Complete the following table 

This table displays the values of two functions, \( f(x) \) and \( g(x) \), along with their compositions \( (f \circ g)(x) \) and \( (g \circ f)(x) \). | \( x \) | \( f(x) \) | \( g(x) \) | \( (f \circ g)(x) \) | \( (g \circ f)(x) \) | |---|---|---|---|---| | 1 | 2 | 5 | | | | 2 | 3 | 6 | | | | 3 | 4 | 1 | | | | 4 | 5 | 2 | | | | 5 | 6 | 3 | | | | 6 | 1 | 4 | | | ### Explanation: - **\( f(x) \):** Represents the function \( f \) applied to \( x \). - **\( g(x) \):** Represents the function \( g \) applied to \( x \). - **\( (f \circ g)(x) \):** Represents the composition of \( f \) and \( g \), which is calculated by applying \( g \) to \( x \) first and then applying \( f \) to the result. - **\( (g \circ f)(x) \):** Represents the composition of \( g \) and \( f \), which is calculated by applying \( f \) to \( x \) first and then applying \( g \) to the result. This table can be used to practice calculating function compositions.
Transcribed Image Text:This table displays the values of two functions, \( f(x) \) and \( g(x) \), along with their compositions \( (f \circ g)(x) \) and \( (g \circ f)(x) \). | \( x \) | \( f(x) \) | \( g(x) \) | \( (f \circ g)(x) \) | \( (g \circ f)(x) \) | |---|---|---|---|---| | 1 | 2 | 5 | | | | 2 | 3 | 6 | | | | 3 | 4 | 1 | | | | 4 | 5 | 2 | | | | 5 | 6 | 3 | | | | 6 | 1 | 4 | | | ### Explanation: - **\( f(x) \):** Represents the function \( f \) applied to \( x \). - **\( g(x) \):** Represents the function \( g \) applied to \( x \). - **\( (f \circ g)(x) \):** Represents the composition of \( f \) and \( g \), which is calculated by applying \( g \) to \( x \) first and then applying \( f \) to the result. - **\( (g \circ f)(x) \):** Represents the composition of \( g \) and \( f \), which is calculated by applying \( f \) to \( x \) first and then applying \( g \) to the result. This table can be used to practice calculating function compositions.
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