Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.1: Relations And Functions
Problem 75PS
Related questions
Question
![### Composite Functions and Data Lookup
To evaluate composite functions given the functions \(f(x)\) and \(g(x)\), you can use the values provided in the following table. This table lists the values of \(f(x)\) and \(g(x)\) for specific values of \(x\).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & -8 & -5 & -2 & 0 & 3 & 4 & 6 & 10 \\
\hline
f(x) & 10 & 4 & 6 & 3 & 0 & -8 & -5 & -2 \\
\hline
g(x) & -2 & 10 & -5 & 6 & -8 & 0 & 4 & 3 \\
\hline
\end{array}
\]
#### Tasks:
1. Find \((f \circ g)(-5)\)
2. Find \((f \circ f)(-2)\)
3. Find \((g \circ f)(10)\)
4. Find \((g \circ g)(4)\)
#### Detailed Steps:
1. **\((f \circ g)(-5)\)**:
- Determine \(g(-5)\) from the table: \(g(-5) = 10\)
- Then, find \(f(g(-5)) = f(10)\):
- From the table, \(f(10) = -2\)
- So, \((f \circ g)(-5) = -2\)
2. **\((f \circ f)(-2)\)**:
- Determine \(f(-2)\) from the table: \(f(-2) = 6\)
- Then, find \(f(f(-2)) = f(6)\):
- From the table, \(f(6) = -5\)
- So, \((f \circ f)(-2) = -5\)
3. **\((g \circ f)(10)\)**:
- Determine \(f(10)\) from the table: \(f(10) = -2\)
- Then, find \(g(f(10)) = g(-2)\):
- From the table, \(g(-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa78a88d7-60f0-4b9e-a272-6ff852667c68%2F374d8c31-ed40-4296-b834-38d4a388d583%2F02drdaj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Composite Functions and Data Lookup
To evaluate composite functions given the functions \(f(x)\) and \(g(x)\), you can use the values provided in the following table. This table lists the values of \(f(x)\) and \(g(x)\) for specific values of \(x\).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & -8 & -5 & -2 & 0 & 3 & 4 & 6 & 10 \\
\hline
f(x) & 10 & 4 & 6 & 3 & 0 & -8 & -5 & -2 \\
\hline
g(x) & -2 & 10 & -5 & 6 & -8 & 0 & 4 & 3 \\
\hline
\end{array}
\]
#### Tasks:
1. Find \((f \circ g)(-5)\)
2. Find \((f \circ f)(-2)\)
3. Find \((g \circ f)(10)\)
4. Find \((g \circ g)(4)\)
#### Detailed Steps:
1. **\((f \circ g)(-5)\)**:
- Determine \(g(-5)\) from the table: \(g(-5) = 10\)
- Then, find \(f(g(-5)) = f(10)\):
- From the table, \(f(10) = -2\)
- So, \((f \circ g)(-5) = -2\)
2. **\((f \circ f)(-2)\)**:
- Determine \(f(-2)\) from the table: \(f(-2) = 6\)
- Then, find \(f(f(-2)) = f(6)\):
- From the table, \(f(6) = -5\)
- So, \((f \circ f)(-2) = -5\)
3. **\((g \circ f)(10)\)**:
- Determine \(f(10)\) from the table: \(f(10) = -2\)
- Then, find \(g(f(10)) = g(-2)\):
- From the table, \(g(-
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