Question: Suppose $f(x)=4-x^2$ and $g(x)=2x+5$. Find the value of $f(g(-2))$.
1. **State the problem:** We need to find the value of the composite function $f(g(-2))$ given $f(x)=4-x^2$ and $g(x)=2x+5$.
2. **Recall the formula for composite functions:** $f(g(x))$ means we first find $g(x)$ and then substitute that result into $f$.
3. **Calculate $g(-2)$:**
$$g(-2) = 2(-2) + 5 = -4 + 5 = 1$$
4. **Substitute $g(-2)$ into $f$:**
$$f(g(-2)) = f(1) = 4 - (1)^2 = 4 - 1 = 3$$
5. **Final answer:** The value of $f(g(-2))$ is $3$.