To evaluate $g(f(7))$, we need to follow these steps:

1. Find $f(7)$:

   • Locate $x = 7$ on the $y = f(x)$ graph (the graph on the left).
   • From observation, at $x = 7$, $f(x)$ appears to be $-6$ (since the graph shows that point).

   Therefore, $f(7) = -6$.

2. Evaluate $g(f(7)) = g(-6)$:

   • Now, locate $x = -6$ on the $y = g(x)$ graph (the graph on the right).
   • From the graph, at $x = -6$, $g(x)$ is approximately $8$ (as indicated by the graph).

   Therefore, $g(f(7)) = g(-6) = 8$.

Answer:

$g(f(7)) = 8$

Would you like further details or have any questions about this solution?

Here are some follow-up questions related to this problem:

1. How do we determine values from a graph accurately?
2. What are composite functions, and how are they generally evaluated?
3. How would the answer change if we were evaluating $f(g(7))$ instead?
4. Can we determine the equation of $f(x)$ and $g(x)$ from these graphs?
5. How can we use transformations to understand the shapes of $f(x)$ and $g(x)$?

Tip: Always ensure that the graph scale is consistent before interpreting values to avoid errors.