https://file.aiquickdraw.com/mathbot/file/1726968186379nb4fmrww.jpg

Let's solve the expressions using the graphs provided for \( f(x) \) and \( g(x) \).

### Step-by-step approach:
1. **For \( f(g(2)) \):**
   - First, find \( g(2) \) using the \( g(x) \) graph. From the graph, \( g(2) = 5 \).
   - Now, substitute this into \( f(x) \) to find \( f(5) \). From the graph, \( f(5) = 3 \).
   - Therefore, \( f(g(2)) = 3 \).

2. **For \( g(f(3)) \):**
   - First, find \( f(3) \) using the \( f(x) \) graph. From the graph, \( f(3) = 3 \).
   - Now, substitute this into \( g(x) \) to find \( g(3) \). From the graph, \( g(3) = 2 \).
   - Therefore, \( g(f(3)) = 2 \).

3. **For \( f(f(0)) \):**
   - First, find \( f(0) \) using the \( f(x) \) graph. From the graph, \( f(0) = 1 \).
   - Now, substitute this into \( f(x) \) to find \( f(1) \). From the graph, \( f(1) = 3 \).
   - Therefore, \( f(f(0)) = 3 \).

4. **For \( g(g(1)) \):**
   - First, find \( g(1) \) using the \( g(x) \) graph. From the graph, \( g(1) = 4 \).
   - Now, substitute this into \( g(x) \) to find \( g(4) \). From the graph, \( g(4) = 1 \).
   - Therefore, \( g(g(1)) = 1 \).

### Final answers:
- \( f(g(2)) = 3 \)
- \( g(f(3)) = 2 \)
- \( f(f(0)) = 3 \)
- \( g(g(1)) = 1 \)

Let me know if you need further clarification or details on any of these steps!

Here are 5 related questions you might want to explore:
1. How do you find the composition of two functions from their graphs?
2. What is the difference between \( f(x) \) and \( f(g(x)) \)?
3. Can you find \( g(f(4)) \) using the graphs provided?
4. How would you approach solving \( f(g(x)) \) for general values of \( x \)?
5. What are the domain and range of the functions \( f(x) \) and \( g(x) \)?

**Tip**: Always start by evaluating the inner function first when dealing with function compositions like \( f(g(x)) \).

Use the graphs to evaluate the expressions: f(g(2)), g(f(3)), f(f(0)), g(g(1)).

Learn how to evaluate compositions of functions using graphs for expressions like f(g(2)) and g(f(3)). This problem involves interpreting function values from graphs and applying function composition.

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