The problem asks you to find the composite function $(f \circ g)(x)$, where the functions $f(x) = x^2 - 4$ and $g(x) = x + 2$ are given.

To compute $(f \circ g)(x)$, you need to substitute $g(x)$ into $f(x)$. This is done as follows:

$(f \circ g)(x) = f(g(x))$

Since $g(x) = x + 2$, substitute this into $f(x) = x^2 - 4$:

$f(g(x)) = f(x + 2)$

Now, apply the expression for $f(x)$:

$f(x + 2) = (x + 2)^2 - 4$

Now, expand $(x + 2)^2$:

$(x + 2)^2 = x^2 + 4x + 4$

So,

$f(x + 2) = x^2 + 4x + 4 - 4$

Simplify:

$f(x + 2) = x^2 + 4x$

Therefore, the composite function is:

$(f \circ g)(x) = x^2 + 4x$

Let me know if you'd like a more detailed explanation or if you have any further questions!

Here are five related questions to explore further:

1. How do you find the inverse of a composite function?
2. What are other properties of composite functions?
3. How do you solve for $x$ if given a composite function equation?
4. How would you calculate $(g \circ f)(x)$ in this case?
5. How does the composition of functions relate to function transformation?

Tip: Always remember that when finding a composite function, you are essentially substituting one function into another!