Answer
(a) $ \sqrt {2x+3}$, domain $\{x|x\ge-\frac{3}{2} \}$.
(b) $ 2\sqrt x+3$, domain $\{x|x\ge0 \}$.
(c) $ \sqrt[4] x$, domain $\{x|x\ge0 \}$.
(d) $ 4x+9$, domain $\{x|x=all\ real\ numbers \}$.
Work Step by Step
Given $f(x)=\sqrt x$ and $g(x)=2x+3$, we have:
(a) $f\circ g=\sqrt {2x+3}$, domain $\{x|x\ge-\frac{3}{2} \}$.
(b) $g\circ f=2\sqrt x+3$, domain $\{x|x\ge0 \}$.
(c) $f\circ f=\sqrt {\sqrt x}=\sqrt[4] x$, domain $\{x|x\ge0 \}$.
(d) $g\circ g=2(2x+3)+3=4x+9$, domain $\{x|x=all\ real\ numbers \}$.
