https://file.aiquickdraw.com/mathbot/file/1726591117683lg219yct.jpg

Let's solve the given questions step by step by analyzing the graphs of the functions \( f(x) \) and \( g(x) \):

### 1. \( f(g(5)) \)
- First, find \( g(5) \) from the graph of \( g(x) \). 
  - On the graph of \( g(x) \), when \( x = 5 \), \( g(5) = 4 \).
- Now, find \( f(4) \) from the graph of \( f(x) \).
  - On the graph of \( f(x) \), when \( x = 4 \), \( f(4) = 0 \).
- So, \( f(g(5)) = f(4) = 0 \).

### 2. \( g(f(1)) \)
- First, find \( f(1) \) from the graph of \( f(x) \).
  - On the graph of \( f(x) \), when \( x = 1 \), \( f(1) = 2 \).
- Now, find \( g(2) \) from the graph of \( g(x) \).
  - On the graph of \( g(x) \), when \( x = 2 \), \( g(2) = 0 \).
- So, \( g(f(1)) = g(2) = 0 \).

### 3. \( f(f(4)) \)
- First, find \( f(4) \) from the graph of \( f(x) \).
  - On the graph of \( f(x) \), when \( x = 4 \), \( f(4) = 0 \).
- Now, find \( f(0) \) from the graph of \( f(x) \).
  - On the graph of \( f(x) \), when \( x = 0 \), \( f(0) = 1 \).
- So, \( f(f(4)) = f(0) = 1 \).

### 4. \( g(g(2)) \)
- First, find \( g(2) \) from the graph of \( g(x) \).
  - On the graph of \( g(x) \), when \( x = 2 \), \( g(2) = 0 \).
- Now, find \( g(0) \) from the graph of \( g(x) \).
  - On the graph of \( g(x) \), when \( x = 0 \), \( g(0) = 1 \).
- So, \( g(g(2)) = g(0) = 1 \).

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

Would you like more details on any of the steps? 

Here are some related questions for further practice:
1. What is \( g(f(5)) \)?
2. What is \( f(g(4)) \)?
3. What is \( f(f(3)) \)?
4. What is \( g(f(2)) \)?
5. What is \( f(g(3)) \)?

**Tip:** Always start by evaluating the innermost function when dealing with compositions of functions.

Evaluate the following function compositions based on the graphs of f(x) and g(x): f(g(5)), g(f(1)), f(f(4)), and g(g(2)).

Learn how to solve function compositions like f(g(5)), g(f(1)), f(f(4)), and g(g(2)) by interpreting graphs of f(x) and g(x). This step-by-step guide is perfect for high school students studying functions and graph interpretation.

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