Answer
$[-2,2]$.
See graph.
Work Step by Step
Step 1. Let $f(x)\le g(x)$, we have $x^4-4\le 3x^2 \Longrightarrow x^4-3x^2-4\le0 \Longrightarrow (x^2+1)(x+2)(x-2)\le0$, identify boundary points as $x=-2,2$.
Step 2. Form intervals $(-\infty,-2],[-2,2],[2,\infty)$.
Step 3. Choose test values for each 1interval $x=-3,0,3$.
Step 4. Test the inequality to get results: $False,\ True,\ False$
Step 5. We have the solution $[-2,2]$.
Step 6. See graph.
