Use the graph to determine the value of each composite function. (hof)(3) = (fog)(4) = h(x)! 90) M --5-4-3-2-1 01234 13 → 153 19 4 5 01 3
Use the graph to determine the value of each composite function. (hof)(3) = (fog)(4) = h(x)! 90) M --5-4-3-2-1 01234 13 → 153 19 4 5 01 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Transcription and Explanation for Educational Website**
---
**Text:**
Use the graph to determine the value of each composite function.
\((h \circ f)(3) =\)
\((f \circ g)(4) =\)
---
**Graphs and Diagrams Explanation:**
The image contains three graphs labeled \(h(x)\), \(g(x)\), and \(f(x)\):
1. **Graph of \(h(x)\):**
- This graph appears in the upper left quadrant.
- \(h(x)\) shows a parabolic shape, opening upwards. It is plotted on a standard Cartesian plane with x-values ranging from approximately \(-5\) to \(5\), and y-values from \(0\) to \(5\).
2. **Graph of \(g(x)\):**
- Located in the upper right quadrant.
- \(g(x)\) resembles a wave pattern with peaks and valleys, indicating periodic behavior. The function has visible oscillations within the same x-values range \([-5, 5]\) and y-values from \(0\) to about \(5\).
3. **Graph of \(f(x)\):**
- This graph is in the lower quadrant, underneath \(h(x)\) and \(g(x)\).
- \(f(x)\) is represented as a straight line. It spans all four quadrants, forming a diagonal through the origin suggesting a linear function.
**To solve for the composite functions:**
- **\((h \circ f)(3)\):**
Evaluate \(f(3)\) using the line graph, then apply the result to \(h(x)\) on its curve.
- **\((f \circ g)(4)\):**
Determine \(g(4)\) using the wave pattern, then use this result to find \(f(x)\) in the line graph.
This exercise demonstrates how to evaluate composite functions by analyzing graphical data efficiently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bafa714-33cc-47c4-a9a5-96cfac78ec18%2Ffae4dbdd-6b15-4197-ac30-94342df7f3bc%2Frdjd55l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Website**
---
**Text:**
Use the graph to determine the value of each composite function.
\((h \circ f)(3) =\)
\((f \circ g)(4) =\)
---
**Graphs and Diagrams Explanation:**
The image contains three graphs labeled \(h(x)\), \(g(x)\), and \(f(x)\):
1. **Graph of \(h(x)\):**
- This graph appears in the upper left quadrant.
- \(h(x)\) shows a parabolic shape, opening upwards. It is plotted on a standard Cartesian plane with x-values ranging from approximately \(-5\) to \(5\), and y-values from \(0\) to \(5\).
2. **Graph of \(g(x)\):**
- Located in the upper right quadrant.
- \(g(x)\) resembles a wave pattern with peaks and valleys, indicating periodic behavior. The function has visible oscillations within the same x-values range \([-5, 5]\) and y-values from \(0\) to about \(5\).
3. **Graph of \(f(x)\):**
- This graph is in the lower quadrant, underneath \(h(x)\) and \(g(x)\).
- \(f(x)\) is represented as a straight line. It spans all four quadrants, forming a diagonal through the origin suggesting a linear function.
**To solve for the composite functions:**
- **\((h \circ f)(3)\):**
Evaluate \(f(3)\) using the line graph, then apply the result to \(h(x)\) on its curve.
- **\((f \circ g)(4)\):**
Determine \(g(4)\) using the wave pattern, then use this result to find \(f(x)\) in the line graph.
This exercise demonstrates how to evaluate composite functions by analyzing graphical data efficiently.
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