Chapter 4 - Polynomial and Rational Functions - 4.4 Polynomial and Rational Inequalities - 4.4 Assess Your Understanding - Page 220: 71

$[-1,1]$ See graph.

Step 1. Let $f(x)\le g(x)$, we have $x^4-1\le -2x^2+2\longrightarrow x^4+2x^2-3\le0 \longrightarrow (x^2+3)(x+1)(x-1)\le0$ Step 2. As $x^2+3\gt0$, we need to solve $(x+1)(x-1)\le0$ or $x^2\le 1$, thus $x\in[-1,1]$ Step 3. See graph for both $f(x)=x^4-1$ and $g(x)=-2x^2+2$.