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