Answer
(a) $ (\frac{2}{5})^{3/2}$.
(b) $ \frac{2}{2^{3/2}+1}$.
(c) $ 1$.
(d) $ \frac{2}{3}$.
Work Step by Step
Given $f(x)=x^{3/2}$ and $g(x)=\frac{2}{x+1}$, we have:
(a) $(f\circ g)(4)=f(g(4))=f(\frac{2}{4+1})=f(\frac{2}{5})=(\frac{2}{5})^{3/2}$.
(b) $(g\circ f)(2)=g(f(2))=g(2^{3/2})=\frac{2}{2^{3/2}+1}$.
(c) $(f\circ f)(1)=f(f(1))=f(1^{3/2})=f(1)=1^{3/2}=1$.
(d) $(g\circ g)(0)=g(g(0))=g(\frac{2}{0+1})=g(2)=\frac{2}{2+1}=\frac{2}{3}$.
