From the image, the problem asks to evaluate $g(f(-1))$ based on the graph provided.

To solve this:

1. We first need to find $f(-1)$ from the graph of $f(x)$.
2. Then, we'll use this value to find $g(f(-1))$ by inputting the result into the graph of $g(x)$.

Let's break it down:

1. Evaluate $f(-1)$: On the graph, trace the point where $x = -1$ on the function $f(x)$ (blue line). Based on the graph, the $y$-value when $x = -1$ gives $f(-1)$.

2. Evaluate $g(f(-1))$: Once we have $f(-1)$, we substitute it into the function $g(x)$ (red line). Find the point on the $g(x)$ graph where the $x$-value equals $f(-1)$, and read the corresponding $y$-value to get $g(f(-1))$.

Let me check the graph and extract the values for you.From the graph:

1. Finding $f(-1)$: When $x = -1$ on the function $f(x)$ (blue line), the corresponding $y$-value appears to be $1$. Therefore, $f(-1) = 1$.

2. Finding $g(f(-1))$: Now that we know $f(-1) = 1$, we use this value in the function $g(x)$ (red line). Looking at the graph of $g(x)$, when $x = 1$, the corresponding $y$-value appears to be $-2$. Therefore, $g(1) = -2$.

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

Would you like more details or have any further questions? Here are some related questions to expand your understanding:

1. What is the domain and range of the functions $f(x)$ and $g(x)$ from the graph?
2. How do you evaluate a composition of functions in general?
3. What is the significance of the order in function composition?
4. Can $g(f(x))$ always be computed for any value of $x$? Why or why not?
5. What are common mistakes when interpreting composed function graphs?

Tip: When dealing with composition of functions, always evaluate the inner function first before proceeding to the outer function.