Use the graphs to evaluate the expressions below. 61 5 4 3 2 1 f(x) 1 f(g(4)) = g(f(5)) = f(f(0)) = g(g(3)) = N 3 X 4 5 6-1 LO 4 3 ܠܟ 2 1 g(x) 1 2 3 4 5 X
Use the graphs to evaluate the expressions below. 61 5 4 3 2 1 f(x) 1 f(g(4)) = g(f(5)) = f(f(0)) = g(g(3)) = N 3 X 4 5 6-1 LO 4 3 ܠܟ 2 1 g(x) 1 2 3 4 5 X
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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Question
![**Using Graphs to Evaluate Composite Functions**
In this lesson, we'll exercise evaluating composite functions using provided graphs for functions \( f(x) \) and \( g(x) \).
**Graphs Overview:**
1. **Graph of \( f(x) \)**:
- \( x \)-axis range: 0 to 6
- \( y \)-axis range: -1 to 6
- The graph points are as follows:
- \( f(1) = 2 \)
- \( f(2) = 4 \)
- \( f(3) = 5 \)
- \( f(4) = 4 \)
- \( f(5) = 2 \)
2. **Graph of \( g(x) \)**:
- \( x \)-axis range: 0 to 6
- \( y \)-axis range: -1 to 6
- The graph points are as follows:
- \( g(1) = 4 \)
- \( g(2) = 2 \)
- \( g(3) = -1 \)
- \( g(4) = 2 \)
- \( g(5) = 4 \)
**Evaluating Composite Functions:**
1. **\( f(g(4)) \)**:
- First, find \( g(4) \):
\[ g(4) = 2 \]
- Next, find \( f(2) \):
\[ f(2) = 4 \]
- Therefore, \( f(g(4)) = f(2) = 4 \).
2. **\( g(f(5)) \)**:
- First, find \( f(5) \):
\[ f(5) = 2 \]
- Next, find \( g(2) \):
\[ g(2) = 2 \]
- Therefore, \( g(f(5)) = g(2) = 2 \).
3. **\( f(f(0)) \)**:
- First, find \( f(0) \):
\( f(0) \) is not explicitly provided in the given graph, implying that additional context or explanation is needed. From the given range, we presume \( f(0) \) is outside the examined range](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa78a88d7-60f0-4b9e-a272-6ff852667c68%2F1d41180d-642b-473b-ab1a-53ff9b0987ee%2Fls4wcoi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Graphs to Evaluate Composite Functions**
In this lesson, we'll exercise evaluating composite functions using provided graphs for functions \( f(x) \) and \( g(x) \).
**Graphs Overview:**
1. **Graph of \( f(x) \)**:
- \( x \)-axis range: 0 to 6
- \( y \)-axis range: -1 to 6
- The graph points are as follows:
- \( f(1) = 2 \)
- \( f(2) = 4 \)
- \( f(3) = 5 \)
- \( f(4) = 4 \)
- \( f(5) = 2 \)
2. **Graph of \( g(x) \)**:
- \( x \)-axis range: 0 to 6
- \( y \)-axis range: -1 to 6
- The graph points are as follows:
- \( g(1) = 4 \)
- \( g(2) = 2 \)
- \( g(3) = -1 \)
- \( g(4) = 2 \)
- \( g(5) = 4 \)
**Evaluating Composite Functions:**
1. **\( f(g(4)) \)**:
- First, find \( g(4) \):
\[ g(4) = 2 \]
- Next, find \( f(2) \):
\[ f(2) = 4 \]
- Therefore, \( f(g(4)) = f(2) = 4 \).
2. **\( g(f(5)) \)**:
- First, find \( f(5) \):
\[ f(5) = 2 \]
- Next, find \( g(2) \):
\[ g(2) = 2 \]
- Therefore, \( g(f(5)) = g(2) = 2 \).
3. **\( f(f(0)) \)**:
- First, find \( f(0) \):
\( f(0) \) is not explicitly provided in the given graph, implying that additional context or explanation is needed. From the given range, we presume \( f(0) \) is outside the examined range
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