Let's evaluate $g(f(-2))$.

Step 1: Compute $f(-2)$

We are given the function: $f(a) = (a + 2)^2$ Substituting $a = -2$: $f(-2) = (-2 + 2)^2 = 0^2 = 0$

Step 2: Compute $g(f(-2)) = g(0)$

We are given: $g(a) = 5a + 4$ Substituting $a = 0$: $g(0) = 5(0) + 4 = 0 + 4 = 4$

Final Answer:

$g(f(-2)) = 4$

Would you like a more detailed breakdown of any step? Here are some related questions to explore:

1. How do you evaluate composite functions in general?
2. What happens if you change the values of $a$ in $f(a)$ and $g(a)$?
3. How can you find the inverse of $f(a)$ or $g(a)$?
4. What are the domain and range of $f(a)$ and $g(a)$?
5. How would you graph these functions and their composition?

Tip: When dealing with composite functions, always evaluate the inner function first before substituting its result into the outer function.