Given two functions $f(x) = 3\sqrt{x}$ and $g(x) = x^4 + 2$, we want to find the composite function $(f \circ g)(x)$, which is equal to $f(g(x))$.

1. Problem Description

Given two functions $f(x) = 3\sqrt{x}$ and $g(x) = x^4 + 2$, we want to find the composite function $(f \circ g)(x)$, which is equal to $f(g(x))$.

2. Solution Steps

The composite function $(f \circ g)(x)$ is defined as $f(g(x))$.

First, substitute $g(x)$ into $f(x)$:

$f(g(x)) = f(x^4 + 2)$.

Now, we replace $x$ in the expression for $f(x)$ with $x^4 + 2$:

$f(x) = 3\sqrt{x}$

$f(x^4+2) = 3\sqrt{x^4 + 2}$.

Thus, $(f \circ g)(x) = 3\sqrt{x^4 + 2}$.

3. Final Answer

The final answer is (C) $3\sqrt{x^4+2}$