If $g(x) = 2x^2 - 3$ and $h(x) = 4x^3 +1$, what is the value of $g(h(-1))$?
I want to find $g(h(-1))$, which means I need to first plug in $x=-1$ into $h(x)$ and then plug in the result into $g(x)$. So let me start by finding $h(-1)$. To do that, I just replace $x$ with $-1$ in the expression for $h(x)$ and simplify. So I get $h(-1) = 4(-1)^3 + 1 = 4(-1) + 1 = -4 + 1 = -3$. Now that I have $h(-1) = -3$, I can plug that into $g(x)$ and simplify. So I get $g(h(-1)) = g(-3) = 2(-3)^2 - 3 = 2(9) - 3 = 18 - 3 = 15$. And that's my final answer. 