College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 124E
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![### 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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