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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![**Problem 7: Using Tables to Find Composite Functions**
**Objective:** Use the provided tables to determine the value of \( (f \circ g)(5) \).
**Tables:**
1. **Table for \( g(x) \):**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 2 & 7 & 1 & 9 & 5 \\
\hline
g(x) & 3 & 4 & 9 & 12 & 6 \\
\hline
\end{array}
\]
- This table shows values of the function \( g(x) \) for specific \( x \) values.
2. **Table for \( f(x) \):**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 9 & 4 & 6 & 12 & 3 \\
\hline
f(x) & 6 & -3 & 7 & 5 & 9 \\
\hline
\end{array}
\]
- This table shows values of the function \( f(x) \) for specific \( x \) values.
**Steps to Solve for \( (f \circ g)(5) \):**
1. **Find \( g(5) \):**
- Locate \( x = 5 \) in the \( g(x) \) table.
- \( g(5) = 6 \).
2. **Find \( f(g(5)) = f(6) \):**
- Use the result from \( g(5) \) to find \( f(6) \) in the \( f(x) \) table.
- \( f(6) = 7 \).
**Conclusion:**
\( (f \circ g)(5) = f(g(5)) = f(6) = 7 \).
Thus, the value of \( (f \circ g)(5) \) is 7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5ceabf9-03c8-41e1-87fc-a1724a9adb6b%2F7c3e7972-a02c-4d5d-865f-0542c4c69c61%2F7jk5ivh_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7: Using Tables to Find Composite Functions**
**Objective:** Use the provided tables to determine the value of \( (f \circ g)(5) \).
**Tables:**
1. **Table for \( g(x) \):**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 2 & 7 & 1 & 9 & 5 \\
\hline
g(x) & 3 & 4 & 9 & 12 & 6 \\
\hline
\end{array}
\]
- This table shows values of the function \( g(x) \) for specific \( x \) values.
2. **Table for \( f(x) \):**
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 9 & 4 & 6 & 12 & 3 \\
\hline
f(x) & 6 & -3 & 7 & 5 & 9 \\
\hline
\end{array}
\]
- This table shows values of the function \( f(x) \) for specific \( x \) values.
**Steps to Solve for \( (f \circ g)(5) \):**
1. **Find \( g(5) \):**
- Locate \( x = 5 \) in the \( g(x) \) table.
- \( g(5) = 6 \).
2. **Find \( f(g(5)) = f(6) \):**
- Use the result from \( g(5) \) to find \( f(6) \) in the \( f(x) \) table.
- \( f(6) = 7 \).
**Conclusion:**
\( (f \circ g)(5) = f(g(5)) = f(6) = 7 \).
Thus, the value of \( (f \circ g)(5) \) is 7.
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