Use the graphs to evaluate the expressions below. (Photo) f(g(5)) = g(f(1)) = f(f(3)) = g(g(2)) =

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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Use the graphs to evaluate the expressions below.

(Photo)

f(g(5)) =

g(f(1)) =

f(f(3)) =

g(g(2)) =

The image contains two line graphs, each illustrating a piecewise linear function.

**Graph of \(f(x)\):**

- **Axes:** The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6.
- **Points:** The graph is composed of linear segments connecting the points:
  - (1, 2)
  - (2, 4)
  - (3, 5)
  - (4, 1)
  - (5, 2)
- **Labeling:** The function is labeled \(f(x)\) in blue near the top left, and the x-axis is labeled with \(x\) in blue at the bottom right.

**Graph of \(g(x)\):**

- **Axes:** The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6.
- **Points:** The graph consists of linear segments connecting the points:
  - (1, 5)
  - (2, 2)
  - (3, 4)
  - (4, 3)
  - (5, 1)
- **Labeling:** The function is labeled \(g(x)\) in blue near the top left, and the x-axis is labeled with \(x\) in blue at the bottom right.

Both graphs share the same grid structure for easy comparison of their behaviors over the specified domain. Each piece connects with straight lines, demonstrating changes in the function's value over specific intervals.
Transcribed Image Text:The image contains two line graphs, each illustrating a piecewise linear function. **Graph of \(f(x)\):** - **Axes:** The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6. - **Points:** The graph is composed of linear segments connecting the points: - (1, 2) - (2, 4) - (3, 5) - (4, 1) - (5, 2) - **Labeling:** The function is labeled \(f(x)\) in blue near the top left, and the x-axis is labeled with \(x\) in blue at the bottom right. **Graph of \(g(x)\):** - **Axes:** The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6. - **Points:** The graph consists of linear segments connecting the points: - (1, 5) - (2, 2) - (3, 4) - (4, 3) - (5, 1) - **Labeling:** The function is labeled \(g(x)\) in blue near the top left, and the x-axis is labeled with \(x\) in blue at the bottom right. Both graphs share the same grid structure for easy comparison of their behaviors over the specified domain. Each piece connects with straight lines, demonstrating changes in the function's value over specific intervals.
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