We are asked to evaluate $f(g(-2))$, using the graphs provided.

Step 1: Find $g(-2)$

From the graph of $y = g(x)$ (the right graph), locate $x = -2$. At $x = -2$, the value of $g(x)$ is the corresponding $y$-coordinate. Based on the graph: $g(-2) = 3$

Step 2: Find $f(g(-2)) = f(3)$

Now, we use this value $g(-2) = 3$ in the function $f(x)$. From the graph of $y = f(x)$ (the left graph), locate $x = 3$. At $x = 3$, the value of $f(x)$ is: $f(3) = -7$

Final Answer:

$f(g(-2)) = -7$

Would you like a more detailed breakdown or any additional questions?

Here are 5 related questions:

1. What is $f(g(2))$?
2. How do we find $g(f(-4))$ using the graphs?
3. What is the domain of $f(x)$ based on the graph?
4. Can we determine if $g(x)$ is a one-to-one function from its graph?
5. How would the answer change if the graph of $f(x)$ or $g(x)$ were shifted vertically?

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