Let's solve $f(f(-2))$, where $f(x) = x^2 + 2x - 3$.

Step 1: Solve for $f(-2)$

We first need to find $f(-2)$ by substituting $x = -2$ into the function $f(x)$.

$f(-2) = (-2)^2 + 2(-2) - 3$ $f(-2) = 4 - 4 - 3$ $f(-2) = -3$

Step 2: Solve for $f(f(-2)) = f(-3)$

Now, substitute $x = -3$ into the function $f(x)$ to get $f(-3)$.

$f(-3) = (-3)^2 + 2(-3) - 3$ $f(-3) = 9 - 6 - 3$ $f(-3) = 0$

Thus, $f(f(-2)) = 0$.

Final Answer:

$f(f(-2)) = 0$

Do you have any questions, or would you like more details?

Here are 5 related questions to expand on this:

1. What is $g(f(-2))$ using the given $g(x)$?
2. Find $h(f(-2))$.
3. Calculate $f(h(-3))$.
4. Solve $f(x) = 0$ for $x$.
5. What is $g(g(-2))$?

Tip: When solving nested functions, break it down step by step by first solving the innermost function, then use that result for the next.