Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.4: More Quadratic Functions And Applications
Problem 55PS
Related questions
Question
![### Problem Statement
Given the functions \( f(x) = 7x - 1 \) and \( g(x) = 7 - x^2 \), calculate the following:
1. \( f(g(0)) \)
2. \( g(f(0)) \)
### Solution
#### Part (a) \( f(g(0)) \)
1. Start by calculating \( g(0) \):
\[
g(0) = 7 - (0)^2 = 7
\]
2. Next, use the result from \( g(0) \) to find \( f(g(0)) \), which is \( f(7) \):
\[
f(7) = 7(7) - 1 = 49 - 1 = 48
\]
Therefore, \( f(g(0)) = 48 \).
#### Part (b) \( g(f(0)) \)
1. Start by calculating \( f(0) \):
\[
f(0) = 7(0) - 1 = -1
\]
2. Next, use the result from \( f(0) \) to find \( g(f(0)) \), which is \( g(-1) \):
\[
g(-1) = 7 - (-1)^2 = 7 - 1 = 6
\]
Therefore, \( g(f(0)) = 6 \).
### Final Answers
**(a) \( f(g(0)) = 48 \)**
**(b) \( g(f(0)) = 6 \)**
These results provide insight into the composite functions involving given functions \( f \) and \( g \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6010960e-f970-4bb2-b167-12f0ced798a6%2F8260ec7f-ece4-47fd-9093-e899f9233a95%2F4zu7dnd.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Given the functions \( f(x) = 7x - 1 \) and \( g(x) = 7 - x^2 \), calculate the following:
1. \( f(g(0)) \)
2. \( g(f(0)) \)
### Solution
#### Part (a) \( f(g(0)) \)
1. Start by calculating \( g(0) \):
\[
g(0) = 7 - (0)^2 = 7
\]
2. Next, use the result from \( g(0) \) to find \( f(g(0)) \), which is \( f(7) \):
\[
f(7) = 7(7) - 1 = 49 - 1 = 48
\]
Therefore, \( f(g(0)) = 48 \).
#### Part (b) \( g(f(0)) \)
1. Start by calculating \( f(0) \):
\[
f(0) = 7(0) - 1 = -1
\]
2. Next, use the result from \( f(0) \) to find \( g(f(0)) \), which is \( g(-1) \):
\[
g(-1) = 7 - (-1)^2 = 7 - 1 = 6
\]
Therefore, \( g(f(0)) = 6 \).
### Final Answers
**(a) \( f(g(0)) = 48 \)**
**(b) \( g(f(0)) = 6 \)**
These results provide insight into the composite functions involving given functions \( f \) and \( g \).
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