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:

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, $f(g(-2)) = f(1) = 4$.

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, $g(f(0)) = g(2) = -1$.

3. $f(-3)$

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

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

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, $g(g(-1)) = g(3) = 2$.

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.

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!