Answer
(a) $ \sqrt {13}$.
(b) $ 3(\sqrt 3)=3\sqrt 3$.
(c) $ \sqrt {\sqrt 2+1}$.
(d) $ 0$.
Work Step by Step
Given $f(x)=\sqrt {x+1}$ and $g(x)=3x$, we have:
(a) $(f\circ g)(4)=f(g(4))=f(3(4))=f(12)=\sqrt {12+1}=\sqrt {13}$.
(b) $(g\circ f)(2)=g(f(2))=g(\sqrt {2+1})=g(\sqrt {3})=3(\sqrt 3)=3\sqrt 3$.
(c) $(f\circ f)(1)=f(f(1))=f(\sqrt {1+1})=f(\sqrt {2})=\sqrt {\sqrt 2+1}$.
(d) $(g\circ g)(0)=g(g(0))=g(3(0))=g(0)=3(0)=0$.
