To solve $(g \circ f)(-5)$, we need to evaluate the composite function step-by-step:

Step 1: Find $f(-5)$

Using the first table, we locate $x = -5$. The corresponding value for $f(x)$ is: $f(-5) = 3$

Step 2: Find $g(f(-5)) = g(3)$

Now that $f(-5) = 3$, we use the second table to find $g(3)$. When $x = 3$, the value of $g(x)$ is: $g(3) = -3$

Final Answer:

Thus, $(g \circ f)(-5) = g(f(-5)) = g(3) = -3$.

$(g \circ f)(-5) = -3$

Let me know if you need further explanation or details!

Here are 5 related questions to explore:

1. How do you evaluate $(f \circ g)(-1)$ using the given tables?
2. What is $g(f(2))$ using the same tables?
3. Can you find $f(f(-5))$ by applying $f$ twice?
4. How do composite functions work if the range of $f$ doesn't match the domain of $g$?
5. What are the domain and range of $f$ and $g$ based on the tables?

Tip: When working with composite functions, always evaluate the inner function first and then use its result as the input for the outer function.