How do I solve The image features two graphs and a series of function evaluations. **Graph Descriptions:**1. **Graph of $ f(x) $:** - This is a line graph plotted in the left coordinate plane. - The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6. - The graph consists of a series of connected line segments with the following notable points: - $ (1, 3) $ - $ (2, 1) $ - $ (3, 5) $ - $ (4, 2) $ - $ (5, 4) $2. **Graph of $ g(x) $:** - Located in the right coordinate plane. - The x-axis spans from -1 to 6, and the y-axis also spans from -1 to 6. - Notable points include: - $ (1, 4) $ - $ (2, 3) $ - $ (3, 1) $ - $ (4, 5) $ - $ (5, 2) $**Function Evaluations:**Below the graphs, there are four equations to solve based on the graphs:1. $ f(g(3)) = $ 2. $ g(f(0)) = $ 3. $ f(f(2)) = $ 4. $ g(g(5)) = $ The interface allows users to submit answers and seek help from an instructor. There is a "Submit Question" button at the bottom.This setup provides an interactive way for students to practice interpreting graphs and evaluating composite functions.

Answered: The image features two graphs and a…

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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The image features two graphs and a series of function evaluations.

**Graph Descriptions:**

1. **Graph of $ f(x) $:**
- This is a line graph plotted in the left coordinate plane.
- The x-axis ranges from -1 to 6, and the y-axis ranges from -1 to 6.
- The graph consists of a series of connected line segments with the following notable points:
- $ (1, 3) $
- $ (2, 1) $
- $ (3, 5) $
- $ (4, 2) $
- $ (5, 4) $

2. **Graph of $ g(x) $:**
- Located in the right coordinate plane.
- The x-axis spans from -1 to 6, and the y-axis also spans from -1 to 6.
- Notable points include:
- $ (1, 4) $
- $ (2, 3) $
- $ (3, 1) $
- $ (4, 5) $
- $ (5, 2) $

**Function Evaluations:**
Below the graphs, there are four equations to solve based on the graphs:

1. $ f(g(3)) = $
2. $ g(f(0)) = $
3. $ f(f(2)) = $
4. $ g(g(5)) = $

The interface allows users to submit answers and seek help from an instructor. There is a "Submit Question" button at the bottom.

This setup provides an interactive way for students to practice interpreting graphs and evaluating composite functions.

Expert Solution

Step 1

To find the composition values ,

$1) f (g (3)) 2) g (f (0)) 3) f (f (2)) 4) g (g (5))$

For finding this values from the graph we have to follow like this:

To find $f (g (a))$ first find the value of $g (a)$ from the graph of $g (x)$ .Let it be d then put this value in $f (g (a))$ i.e. $f (d)$ & then find the value of $f (d)$ from the graph of $f (x)$ , which is the final answer of $f (g (a))$ .

Similarly ,To find $g (f (a))$ first find the value of $f (a)$ from the graph of $f (x)$ .Let it be d then put this value in $g (f (a))$ i.e. $g (d)$ & then find the value of $g (d)$ from the graph of $g (x)$ , which is the final answer of $g (f (a))$ .

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