Given the functions $\small{f(x) = \sqrt{x-3}}$ and $\small{g(x) = \sqrt{x^{2}+3}}$, find $\small{(f \circ g)(x)}$ and $\small{(g \circ f)(x)}$ and state the domains of each of the compositions. Enter the domains using interval notation. Use U for the union of sets and inf for $\small{\infty}$.

$\small{(f \circ g)(x)}$	=
Domain	=

$\small{(g \circ f)(x)}$	=
Domain	=