Answer
(a) $\sqrt {\frac{3}{x+6}}$, domain: $(-6,\infty)$
(b) $\frac{3}{\sqrt x+6}$, domain: $[0,\infty)$
Work Step by Step
(a) Given $f(x)=\sqrt {x}, x\ge0$ and $g(x)=\frac{3}{x+6}, x\ne-6$, we have $(f\circ g)(x)=f(g(x))=\sqrt {\frac{3}{x+6}}$. From $x+6\gt0$, we have $x\gt-6$. Combine all the conditions, we can find its domain: $(-6,\infty)$
(b) $(g\circ f)(x)=g(f(x))=\frac{3}{\sqrt x+6}$. Combine all the conditions, we can find its domain: $[0,\infty)$
