Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Composition of Functions (f ∘ g)(−1)
In this problem, we are given function values for \( f \) and \( g \) in a table. The goal is to evaluate the expression \( (f \circ g)(−1) \).
The notation \( (f \circ g)(x) \) represents the composite function, which means \( f(g(x)) \).
Let's use the provided table to find the value of \( (f \circ g)(−1) \). Follow these steps:
1. **Find \( g(−1) \)**:
Locate \( x \) in the table and find its corresponding \( g(x) \).
From the table, when \( x = -1 \):
\[
g(-1) = 0
\]
2. **Find \( f(g(−1)) \)**:
Next, we need to find \( f(g(-1)) = f(0) \).
From the table, when \( x = 0 \):
\[
f(0) = 5
\]
Therefore, \( (f \circ g)(-1) = f(0) = 5 \).
### Table
The table below provides function values for \( f(x) \) and \( g(x) \) at different \( x \) values:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| f(x)| 11 | 9 | 7 | 5 | 3 | 1 | -1 |
| g(x)| -10 | -4 | 0 | 2 | 2 | 0 | -4 |
Use this table to find the necessary function values to evaluate composite functions like \( (f \circ g)(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4895c6df-eb5a-4830-9b1e-b00e9a38873d%2Ff9be4fbd-56ad-4743-94cc-ebae29341877%2Ff8hfju_processed.png&w=3840&q=75)
Transcribed Image Text:### Composition of Functions (f ∘ g)(−1)
In this problem, we are given function values for \( f \) and \( g \) in a table. The goal is to evaluate the expression \( (f \circ g)(−1) \).
The notation \( (f \circ g)(x) \) represents the composite function, which means \( f(g(x)) \).
Let's use the provided table to find the value of \( (f \circ g)(−1) \). Follow these steps:
1. **Find \( g(−1) \)**:
Locate \( x \) in the table and find its corresponding \( g(x) \).
From the table, when \( x = -1 \):
\[
g(-1) = 0
\]
2. **Find \( f(g(−1)) \)**:
Next, we need to find \( f(g(-1)) = f(0) \).
From the table, when \( x = 0 \):
\[
f(0) = 5
\]
Therefore, \( (f \circ g)(-1) = f(0) = 5 \).
### Table
The table below provides function values for \( f(x) \) and \( g(x) \) at different \( x \) values:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| f(x)| 11 | 9 | 7 | 5 | 3 | 1 | -1 |
| g(x)| -10 | -4 | 0 | 2 | 2 | 0 | -4 |
Use this table to find the necessary function values to evaluate composite functions like \( (f \circ g)(x) \).
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