College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 82E
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Question
QUESTION 12
Please do step by step with understandable handwriting please!
![### Find the Requested Function Value
Given the functions:
\[ f(x) = \frac{x - 9}{4} \]
\[ g(x) = 2x + 1 \]
We need to find \( (g \circ f)(33) \), which means we first apply the function \( f \) to \( 33 \), and then apply the function \( g \) to the result.
### Solution
1. **Find \( f(33) \):**
\[ f(33) = \frac{33 - 9}{4} = \frac{24}{4} = 6 \]
2. **Find \( g(6) \):**
\[ g(6) = 2(6) + 1 = 12 + 1 = 13 \]
Thus, the value of \( (g \circ f)(33) \) is \( 13 \).
### Multiple Choice Answers
- A. \(\frac{29}{2}\)
- B. \(402\)
- C. \(13\) <!-- Correct Answer -->
- D. \(18\)
Correct answer: **C. 13**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e2935af-1329-4dfa-9560-8781a8a0c5be%2F47fe55a6-df42-4b74-bf85-636cde254227%2Fiv3t7x_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the Requested Function Value
Given the functions:
\[ f(x) = \frac{x - 9}{4} \]
\[ g(x) = 2x + 1 \]
We need to find \( (g \circ f)(33) \), which means we first apply the function \( f \) to \( 33 \), and then apply the function \( g \) to the result.
### Solution
1. **Find \( f(33) \):**
\[ f(33) = \frac{33 - 9}{4} = \frac{24}{4} = 6 \]
2. **Find \( g(6) \):**
\[ g(6) = 2(6) + 1 = 12 + 1 = 13 \]
Thus, the value of \( (g \circ f)(33) \) is \( 13 \).
### Multiple Choice Answers
- A. \(\frac{29}{2}\)
- B. \(402\)
- C. \(13\) <!-- Correct Answer -->
- D. \(18\)
Correct answer: **C. 13**
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