Let's evaluate the two expressions step by step using the provided table.

1. For $f(g(-3))$:

   • First, find $g(-3)$. According to the table, $g(-3) = -1$.
   • Next, find $f(-1)$. From the table, $f(-1) = 2$.

   So, $f(g(-3)) = f(-1) = 2$.

2. For $g(f(4))$:

   • First, find $f(4)$. According to the table, $f(4) = -3$.
   • Next, find $g(-3)$. From the table, $g(-3) = -1$.

   So, $g(f(4)) = g(-3) = -1$.

Final Results:

• $f(g(-3)) = 2$
• $g(f(4)) = -1$

Would you like more details or have any questions? Here are some related questions you can explore:

1. How do you compose functions like $f(g(x))$ for different values of $x$?
2. Can you explain why composing functions involves applying one function after the other?
3. How would you evaluate $g(g(-3))$ using the table?
4. How do function tables help in understanding function composition?
5. Can you find $f(f(5))$ using the table?

Tip: When composing functions, always start with the innermost function and work outward.