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

Question

UpStudy AI · Accepted Answer

To find the value of $$ f(g(-2)) $$, we'll follow these steps:

1. **Calculate $$ g(-2) $$:**
   
   Given $$ g(x) = 3x + 5 $$,
   $$
   g(-2) = 3(-2) + 5 = -6 + 5 = -1
   $$

2. **Now, calculate $$ f(g(-2)) = f(-1) $$:**
   
   Given $$ f(x) = 4 - x^2 $$,
   $$
   f(-1) = 4 - (-1)^2 = 4 - 1 = 3
   $$

**Answer:** $$ 3 $$
$$ f(g(-2)) = 3 $$

Consider the functions and .
Find the value of .