https://file.aiquickdraw.com/mathbot/file/1730215847146cjidilq4.jpg

Let's analyze the graphs and evaluate each of the expressions step-by-step.

1. **For** \( f(g(5)) \):
   - First, find \( g(5) \) on the graph of \( g(x) \). When \( x = 5 \), \( g(5) = 4 \).
   - Next, use \( f(4) \) on the graph of \( f(x) \). When \( x = 4 \), \( f(4) = 2 \).
   - So, \( f(g(5)) = f(4) = 2 \).

2. **For** \( g(f(4)) \):
   - First, find \( f(4) \) on the graph of \( f(x) \). We already know from the previous step that \( f(4) = 2 \).
   - Next, use \( g(2) \) on the graph of \( g(x) \). When \( x = 2 \), \( g(2) = 1 \).
   - Thus, \( g(f(4)) = g(2) = 1 \).

3. **For** \( f(f(2)) \):
   - First, find \( f(2) \) on the graph of \( f(x) \). When \( x = 2 \), \( f(2) = 5 \).
   - Next, use \( f(5) \) on the graph of \( f(x) \). When \( x = 5 \), \( f(5) = 1 \).
   - Therefore, \( f(f(2)) = f(5) = 1 \).

4. **For** \( g(g(1)) \):
   - First, find \( g(1) \) on the graph of \( g(x) \). When \( x = 1 \), \( g(1) = 3 \).
   - Next, use \( g(3) \) on the graph of \( g(x) \). When \( x = 3 \), \( g(3) = 0 \).
   - So, \( g(g(1)) = g(3) = 0 \).

### Final Answers:
- \( f(g(5)) = 2 \)
- \( g(f(4)) = 1 \)
- \( f(f(2)) = 1 \)
- \( g(g(1)) = 0 \)

Would you like further details on any of these steps? 

Here are some related questions for additional practice:
1. What is \( f(g(3)) \)?
2. What is \( g(f(1)) \)?
3. What is \( f(f(5)) \)?
4. What is \( g(g(4)) \)?
5. How would you find \( g(f(5)) \)?

**Tip:** For composite functions like \( f(g(x)) \), evaluate the inner function first, then use its result to find the value of the outer function.

Use the graphs to evaluate the following composite function expressions: f(g(5)), g(f(4)), f(f(2)), and g(g(1)).

Learn how to evaluate composite functions such as f(g(5)) and g(f(4)) using graphs. This step-by-step guide walks through the function composition process by interpreting function graphs. Suitable for high school students studying algebra and functions.

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