We are given two functions, $f(x) = 3x - 1$ and $g(x) = 2x^3$. We need to evaluate $f(g(-2))$.

1. Problem Description

We are given two functions, $f(x) = 3x - 1$ and $g(x) = 2x^3$. We need to evaluate $f(g(-2))$.

2. Solution Steps

First, we need to find the value of $g(-2)$.

We substitute $x = -2$ into the expression for $g(x)$:

$g(x) = 2x^3$

$g(-2) = 2(-2)^3$

$g(-2) = 2(-8)$

$g(-2) = -16$

Next, we need to find the value of $f(g(-2))$. Since $g(-2) = -16$, we need to find $f(-16)$.

We substitute $x = -16$ into the expression for $f(x)$:

$f(x) = 3x - 1$

$f(-16) = 3(-16) - 1$

$f(-16) = -48 - 1$

$f(-16) = -49$

Therefore, $f(g(-2)) = -49$.

3. Final Answer

-49