Consider the functions \( f(x)=4-x^{2} \) and \( g(x)=3 x+5 \). Find the value of \( f(g(-2)) \). \( \begin{array}{l}5 \\ 3 \\ 1\end{array} \)

To find \( f(g(-2)) \), we first need to compute \( g(-2) \). Using the function \( g(x) = 3x + 5 \): \[ g(-2) = 3(-2) + 5 = -6 + 5 = -1 \] Now that we have \( g(-2) = -1 \), we can compute \( f(g(-2)) = f(-1) \). Using the function \( f(x) = 4 - x^{2} \): \[ f(-1) = 4 - (-1)^{2} = 4 - 1 = 3 \] Therefore, the value of \( f(g(-2)) \) is \( 3 \). In conclusion, the answer is \( \boxed{3} \).