Answer
(a) $ \frac{3}{\sqrt[3] 4+1}$.
(b) $ 1$.
(c) $ \frac{6}{5}$.
(d) $ 0$.
Work Step by Step
Given $f(x)=\frac{3}{x+1}$ and $g(x)=\sqrt[3] x$, we have:
(a) $(f\circ g)(4)=f(g(4))=f(\sqrt[3] 4)=\frac{3}{\sqrt[3] 4+1}$.
(b) $(g\circ f)(2)=g(f(2))=g(\frac{3}{2+1})=g(1)=\sqrt[3] 1=1$.
(c) $(f\circ f)(1)=f(f(1))=f(\frac{3}{2+1})=f(\frac{3}{2})=\frac{3}{\frac{3}{2}+1}=\frac{6}{5}$.
(d) $(g\circ g)(0)=g(g(0))=g(\sqrt[3] 0)=g(0)=\sqrt[3] 0=0$.
