Answer
(a) $ \frac{2x+7}{2x+3}$, $\{x|x\ne-\frac{3}{2} \}$.
(b) $ 5$.
(c) $ -3$.
Work Step by Step
Given $f(x)=\frac{x+2}{x-2}$ and $g(x)=2x+5$, we have:
(a) $(f\circ g)(x)=\frac{(2x+5)+2}{(2x+5)-2}=\frac{2x+7}{2x+3}$ with domain $\{x|x\ne-\frac{3}{2} \}$.
(b) $(g\circ f)(-2)=g(\frac{-2+2}{-2-2})=g(0)=5$.
(c) $(f\circ g)(-2)=\frac{2(-2)+7}{2(-2)+3}=-3$.
