Answer
$\{x| x\le0\ or\ x\gt3\}$.
Work Step by Step
Step 1. Domain of $g(x)$: $\{x|x\ne3 \}$.
Step 2. For $(f\circ g)(x)$ we need: $g(x)\ge0 \Longrightarrow \frac{x}{x-3}\ge0 \Longrightarrow x\le0\ or\ x\gt3$.
Step 3. Thus Domain of $(f\circ g)(x)$: $\{x| x\le0\ or\ x\gt3\}$.
