Answer
$(G ∘ G)(x) =\frac{x-2}{-2x+5}$
the domain is $x \ne 2.5$
Work Step by Step
$G(x) = \frac{1}{(x-2)}$
$(G ∘ G)(x) = G(G(x)) = G(\frac{1}{(x-2)}) =\frac{1}{(\frac{1}{(x-2)}-2)}=\frac{1}{\frac{1-2x+4}{x-2}}=\frac{1}{\frac{-2x+5}{x-2}}=\frac{x-2}{-2x+5}$
Therefore the domain is
$-2x + 5 \ne 0 $
$-2x \ne -5 $
$x \ne 2.5$
