College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...
Related questions
Question
![### Composite Function Problem
#### Question:
Given the functions \( f(x) = 2x + 1 \) and \( g(x) = x^2 \), find \( g(f(3)) \).
#### Options:
a. 49
b. 19
c. 7
d. 13
*(Four radio buttons are shown below the options for the user to select the correct answer)*
#### Solution:
To solve this problem, we need to follow these steps:
1. **Evaluate \( f(3) \)**:
\[
f(x) = 2x + 1
\]
Substitute \( x = 3 \):
\[
f(3) = 2(3) + 1 = 6 + 1 = 7
\]
2. **Evaluate \( g(f(3)) \) where \( f(3) = 7 \)**:
\[
g(x) = x^2
\]
Substitute \( x = 7 \):
\[
g(7) = 7^2 = 49
\]
Therefore, \( g(f(3)) = 49 \).
#### Correct Answer:
a. 49](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F349e5e36-2d82-4a9b-b36b-acebde7ec7cc%2Fa9371b58-724e-4cf6-90fd-859fe2cc46f2%2Fj47i40q_processed.png&w=3840&q=75)
Transcribed Image Text:### Composite Function Problem
#### Question:
Given the functions \( f(x) = 2x + 1 \) and \( g(x) = x^2 \), find \( g(f(3)) \).
#### Options:
a. 49
b. 19
c. 7
d. 13
*(Four radio buttons are shown below the options for the user to select the correct answer)*
#### Solution:
To solve this problem, we need to follow these steps:
1. **Evaluate \( f(3) \)**:
\[
f(x) = 2x + 1
\]
Substitute \( x = 3 \):
\[
f(3) = 2(3) + 1 = 6 + 1 = 7
\]
2. **Evaluate \( g(f(3)) \) where \( f(3) = 7 \)**:
\[
g(x) = x^2
\]
Substitute \( x = 7 \):
\[
g(7) = 7^2 = 49
\]
Therefore, \( g(f(3)) = 49 \).
#### Correct Answer:
a. 49
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