Let's analyze the graphs and solve each composition of functions one by one.

1. $f(g(-1))$

• First, we need to find $g(-1)$ from the graph of $g(x)$ (on the right). From the graph, when $x = -1$, $g(-1) = 3$.
• Now, use this value in $f(x)$. We need to find $f(3)$ from the graph of $f(x)$ (on the left). From the graph, when $x = 3$, $f(3) = 2$.
• Therefore, $f(g(-1)) = f(3) = 2$.

2. $g(f(-4))$

• First, find $f(-4)$ from the graph of $f(x)$ (on the left). From the graph, when $x = -4$, $f(-4) = -5$.
• Now, use this value in $g(x)$. We need to find $g(-5)$ from the graph of $g(x)$ (on the right). From the graph, when $x = -5$, $g(-5) = 5$.
• Therefore, $g(f(-4)) = g(-5) = 5$.

3. $f(f(0))$

• First, find $f(0)$ from the graph of $f(x)$ (on the left). From the graph, when $x = 0$, $f(0) = -3$.
• Now, use this value in $f(x)$ again. We need to find $f(-3)$. From the graph, when $x = -3$, $f(-3) = 1$.
• Therefore, $f(f(0)) = f(-3) = 1$.

4. $g(g(-3))$

• First, find $g(-3)$ from the graph of $g(x)$ (on the right). From the graph, when $x = -3$, $g(-3) = 3$.
• Now, use this value in $g(x)$ again. We need to find $g(3)$. From the graph, when $x = 3$, $g(3) = -3$.
• Therefore, $g(g(-3)) = g(3) = -3$.

Final Answers:

1. $f(g(-1)) = 2$
2. $g(f(-4)) = 5$
3. $f(f(0)) = 1$
4. $g(g(-3)) = -3$

Do you want any detailed explanations for these steps?

Here are 5 related questions for further exploration:

1. What is $f(g(2))$?
2. What is $g(f(-2))$?
3. Find $f(g(0))$.
4. Calculate $f(f(4))$.
5. Determine $g(f(2))$.

Tip: When working with compositions of functions, always evaluate the inner function first before moving to the outer one!