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
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
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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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