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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![**Exercise: Expressing Functions in Composite Form**
Express the function in the form \( f \circ g \). (Use non-identity functions for \( f \) and \( g \).)
\[ F(x) = (3x + x^2)^4 \]
\[
\{ f(x), g(x) \} = \{ \ \}
\]
In this exercise, you are tasked with expressing the given function \( F(x) \) as a composition of two functions, \( f(x) \) and \( g(x) \), such that \( F(x) = f(g(x)) \). The functions \( f \) and \( g \) must not be identity functions, meaning they must perform some transformation and not simply return their input. Consider expressing the inner expression separately and the outer transformation to achieve this composition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb7327e-adf7-4bbc-a708-e987be622d92%2Fbe64bafb-2d50-40da-8613-19a12cde3cbf%2Fdcycrb8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise: Expressing Functions in Composite Form**
Express the function in the form \( f \circ g \). (Use non-identity functions for \( f \) and \( g \).)
\[ F(x) = (3x + x^2)^4 \]
\[
\{ f(x), g(x) \} = \{ \ \}
\]
In this exercise, you are tasked with expressing the given function \( F(x) \) as a composition of two functions, \( f(x) \) and \( g(x) \), such that \( F(x) = f(g(x)) \). The functions \( f \) and \( g \) must not be identity functions, meaning they must perform some transformation and not simply return their input. Consider expressing the inner expression separately and the outer transformation to achieve this composition.
![**Problem Statement:**
Find \( f \circ g \circ h \).
**Given Functions:**
- \( f(x) = \tan(x) \)
- \( g(x) = \frac{x}{x - 3} \)
- \( h(x) = \sqrt[3]{x} \)
**Expression to Evaluate:**
\[
\left(\frac{6\pi n + 3\pi}{2\pi n + \pi - 2}\right)^3 \quad \text{(incorrect solution)}
\]
**Explanation:**
We are tasked with finding the composite function \( f(g(h(x))) \). Start by substituting \( h(x) \) into \( g(x) \), and then substitute that result into \( f(x) \).
**Note:** The boxed expression represents an incorrect attempt or result related to the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb7327e-adf7-4bbc-a708-e987be622d92%2Fbe64bafb-2d50-40da-8613-19a12cde3cbf%2Fp4ikmyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( f \circ g \circ h \).
**Given Functions:**
- \( f(x) = \tan(x) \)
- \( g(x) = \frac{x}{x - 3} \)
- \( h(x) = \sqrt[3]{x} \)
**Expression to Evaluate:**
\[
\left(\frac{6\pi n + 3\pi}{2\pi n + \pi - 2}\right)^3 \quad \text{(incorrect solution)}
\]
**Explanation:**
We are tasked with finding the composite function \( f(g(h(x))) \). Start by substituting \( h(x) \) into \( g(x) \), and then substitute that result into \( f(x) \).
**Note:** The boxed expression represents an incorrect attempt or result related to the problem.
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