For the pair of functions, find the indicated composition. 7 2 -=-=-=5.9(x)= 7x f(x) Find (fog)(x). O A. B. C. O D. 49x 2 + 35x 2x - 10 49x 49x 2-35x 7x 2 - 35x
For the pair of functions, find the indicated composition. 7 2 -=-=-=5.9(x)= 7x f(x) Find (fog)(x). O A. B. C. O D. 49x 2 + 35x 2x - 10 49x 49x 2-35x 7x 2 - 35x
Calculus: Early Transcendentals
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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 13
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![# Composition of Functions - Educational Exercise
## Problem Statement:
For the pair of functions, find the indicated composition.
Given:
\[ f(x) = \frac{7}{x - 5} \]
\[ g(x) = \frac{2}{7x} \]
Find \( (f \circ g)(x) \).
### Multiple Choice Options:
A. \( \frac{49x}{2 + 35x} \)
B. \( \frac{2x - 10}{49x} \)
C. \( \frac{49x}{2 - 35x} \)
D. \( \frac{7x}{2 - 35x} \)
### Explanation of Options:
This is a multiple-choice question where you are asked to find the composition \( (f \circ g)(x) \), which means \( f(g(x)) \). You are to choose the correct option from the given answers.
To solve this, substitute \( g(x) \) into \( f(x) \):
1. Start with the function \( g(x) \):
\[ g(x) = \frac{2}{7x} \]
2. Substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f\left( \frac{2}{7x} \right) = \frac{7}{\left(\frac{2}{7x}\right) - 5} \]
3. Simplify the expression inside the function \( f \):
\[ f\left( \frac{2}{7x} \right) = \frac{7}{\frac{2}{7x} - 5} = \frac{7}{\frac{2}{7x} - \frac{35x}{7x}} = \frac{7}{\frac{2 - 35x}{7x}} = 7 \cdot \frac{7x}{2 - 35x} = \frac{49x}{2 - 35x} \]
Thus, the correct answer is:
\[ \boxed{C} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e2935af-1329-4dfa-9560-8781a8a0c5be%2F4cf1fb8f-b9b7-44d0-a39f-fd2b5d7f3c1f%2Fo01lp2_processed.png&w=3840&q=75)
Transcribed Image Text:# Composition of Functions - Educational Exercise
## Problem Statement:
For the pair of functions, find the indicated composition.
Given:
\[ f(x) = \frac{7}{x - 5} \]
\[ g(x) = \frac{2}{7x} \]
Find \( (f \circ g)(x) \).
### Multiple Choice Options:
A. \( \frac{49x}{2 + 35x} \)
B. \( \frac{2x - 10}{49x} \)
C. \( \frac{49x}{2 - 35x} \)
D. \( \frac{7x}{2 - 35x} \)
### Explanation of Options:
This is a multiple-choice question where you are asked to find the composition \( (f \circ g)(x) \), which means \( f(g(x)) \). You are to choose the correct option from the given answers.
To solve this, substitute \( g(x) \) into \( f(x) \):
1. Start with the function \( g(x) \):
\[ g(x) = \frac{2}{7x} \]
2. Substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f\left( \frac{2}{7x} \right) = \frac{7}{\left(\frac{2}{7x}\right) - 5} \]
3. Simplify the expression inside the function \( f \):
\[ f\left( \frac{2}{7x} \right) = \frac{7}{\frac{2}{7x} - 5} = \frac{7}{\frac{2}{7x} - \frac{35x}{7x}} = \frac{7}{\frac{2 - 35x}{7x}} = 7 \cdot \frac{7x}{2 - 35x} = \frac{49x}{2 - 35x} \]
Thus, the correct answer is:
\[ \boxed{C} \]
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