https://file.aiquickdraw.com/mathbot/file/1726808204227fzicn0xp.jpg

Let's solve the function composition problems from the graph provided in your image.

### We have two graphs:
- \( f(x) \) (left graph)
- \( g(x) \) (right graph)

#### First, I'll evaluate each of the given expressions step by step:

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### 1. \( f(g(-2)) \)

- Look at \( g(x) \) on the right graph:
  - When \( x = -2 \), \( g(-2) = 1 \).
  
- Now evaluate \( f(1) \) using the left graph:
  - When \( x = 1 \), \( f(1) = 4 \).

So, \( f(g(-2)) = f(1) = 4 \).

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### 2. \( g(f(0)) \)

- Look at \( f(x) \) on the left graph:
  - When \( x = 0 \), \( f(0) = 2 \).
  
- Now evaluate \( g(2) \) using the right graph:
  - When \( x = 2 \), \( g(2) = -1 \).

So, \( g(f(0)) = g(2) = -1 \).

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### 3. \( f(-3) \)

- Look directly at \( f(x) \) on the left graph:
  - When \( x = -3 \), \( f(-3) = -2 \).

So, \( f(-3) = -2 \).

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### 4. \( g(g(-1)) \)

- Look at \( g(x) \) on the right graph:
  - When \( x = -1 \), \( g(-1) = 3 \).
  
- Now evaluate \( g(3) \) using the right graph:
  - When \( x = 3 \), \( g(3) = 2 \).

So, \( g(g(-1)) = g(3) = 2 \).

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

Let me know if you have any questions or need further clarification.

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Here are 5 additional questions based on this problem:
1. How would you evaluate \( g(f(2)) \)?
2. What is the value of \( f(g(1)) \)?
3. If \( f(x) = g(x) \), what is the value of \( f(x) \) at \( x = -1 \)?
4. What is the result of \( g(f(-2)) \)?
5. How does the composition of functions change if \( f(x) \) is a quadratic function?

**Tip:** Remember, function composition means substituting the output of one function into the input of another. Be sure to evaluate each function step by step carefully!

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

Evaluate function composition problems f(g(-2)), g(f(0)), f(-3), and g(g(-1)) using graphs of f(x) and g(x). Detailed steps provided, suitable for high school math students in Grades 9-12. Learn key concepts in graph interpretation and function composition.

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