The problem asks to find the composite function $h(g(x))$, given $g(x) = 2x + 1$ and $h(x) = 3x - 2$.

1. Problem Description

The problem asks to find the composite function $h(g(x))$, given $g(x) = 2x + 1$ and $h(x) = 3x - 2$.

2. Solution Steps

We need to find $h(g(x))$, which means we need to substitute $g(x)$ into $h(x)$.

Given $g(x) = 2x + 1$ and $h(x) = 3x - 2$.

Substitute $g(x)$ into $h(x)$:

$h(g(x)) = h(2x + 1)$

Now, replace $x$ in the expression for $h(x)$ with $(2x + 1)$:

$h(2x + 1) = 3(2x + 1) - 2$

Expand the expression:

$h(2x + 1) = 6x + 3 - 2$

Simplify the expression:

$h(2x + 1) = 6x + 1$

3. Final Answer

$h(g(x)) = 6x + 1$