To solve $g(f(-1))$, we first need to determine the values of $f(-1)$ and then substitute that value into $g(x)$.

Step-by-step solution:

1. Find $f(-1)$:

   • From the graph, look at the curve for $y = f(x)$ and locate $x = -1$.
   • At $x = -1$, the value of $f(-1)$ is $6$, because the curve passes through the point $(-1, 6)$.

2. Find $g(f(-1)) = g(6)$:

   • Now we need to find $g(6)$.
   • From the graph, look at the curve for $y = g(x)$ and locate $x = 6$.
   • At $x = 6$, the value of $g(6)$ is $-2$, because the curve passes through the point $(6, -2)$.

Therefore, $g(f(-1)) = g(6) = -2$.

Final Answer:

$g(f(-1)) = -2$

Let me know if you'd like more details or have any questions!

Here are 5 related questions:

1. How do you find the composite function $g(f(x))$ for other values of $x$?
2. What is the general process for reading function values from a graph?
3. How can you determine if a graph represents a one-to-one function?
4. What is the domain and range of each function from the graph?
5. How do transformations (shifts, stretches) affect the shape of $f(x)$ or $g(x)$?

Tip: When reading a graph, ensure you pay attention to the labeling of the axes and the curve's behavior at specific points to avoid errors.