Answer
$\{x|x\ge-\frac{3}{2}\}$.
Work Step by Step
Step 1. Domain of $g(x)$: $\{x|x=all\ real\ numbers \}$.
Step 2. For $(f\circ g)(x)$ we need: $g(x)\ge0 \Longrightarrow 2x+3\ge0 \Longrightarrow x\ge-\frac{3}{2}$.
Step 3. Thus Domain of $(f\circ g)(x)$: $\{x|x\ge-\frac{3}{2}\}$.
