Answer
$[0,\frac{1}{3}]$ or $\{x|0\le x\le\frac{1}{3}\}$.
Work Step by Step
Step 1. The domain requirement is $x-3x^2\ge0 \longrightarrow 3x^2-x\le0 \longrightarrow x(3x-1)\le0$.
Step 2. Identify boundary points $x=0,\frac{1}{3}$ and form intervals $(-\infty,0],[0,\frac{1}{3}],[\frac{1}{3},\infty)$.
Step 3. Choose test values $x=-1,0.1,1$ to test the inequality and get results $False,\ True,\ False$.
Step 4. Thus we have the solution $[0,\frac{1}{3}]$ or $\{x|0\le x\le\frac{1}{3}\}$.
