Let $f(x)=x^3+3$ and $g(x) = 2x^2 + 2x +1$. What is $g(f(-2))$?
To find $g(f(-2))$, I need to first evaluate $f(-2)$ by plugging in $-2$ for $x$ in the definition of $f(x)$. I get $f(-2) = (-2)^3 + 3 = -8 + 3 = -5$. So, $g(f(-2))$ is the same as $g(-5)$. Now, I need to evaluate $g(-5)$ by plugging in $-5$ for $x$ in the definition of $g(x)$. I get $g(-5) = 2(-5)^2 + 2(-5) + 1 = 2(25) - 10 + 1 = 50 - 10 + 1 = 41$. 