Answer
(a) $ \frac{3x}{2-x}$, domain $\{x|x\ne0,2 \}$.
(b) $ \frac{2x-2}{3}$, domain $\{x|x\ne1 \}$.
(c) $ \frac{3x-3}{4-x}$, domain $\{x|x\ne1,4 \}$.
(d) $ x$, domain $\{x|x\ne0 \}$.
Work Step by Step
Given $f(x)=\frac{3}{x-1}$ and $g(x)=\frac{2}{x}$, we have:
(a) $f\circ g=\frac{3}{(\frac{2}{x})-1}=\frac{3x}{2-x}$, domain $\{x|x\ne0,2 \}$.
(b) $g\circ f=\frac{2}{\frac{3}{x-1}}=\frac{2x-2}{3}$, domain $\{x|x\ne1 \}$.
(c) $f\circ f=\frac{3}{(\frac{3}{x-1})-1}=\frac{3x-3}{4-x}$, domain $\{x|x\ne1,4 \}$.
(d) $g\circ g=\frac{2}{\frac{2}{x}}=x$, domain $\{x|x\ne0 \}$.
