Answer
a) $\sqrt{13}$; b) $3\sqrt 3$; c) $\sqrt{\sqrt 2+1}$; d) 0.
Work Step by Step
We are given the functions:
$f(x)=\sqrt {x+1}$
$g(x)=3x$
a) $(f\circ g)(4)=f(g(4))=f\left(3(4)\right)=f(12)=\sqrt {12+1}=\sqrt{13}$
b) $(g\circ f)(2)=g(f(2))=g(\sqrt {2+1})=g(\sqrt 3)=3\sqrt 3$
c) $(f\circ f)(1)=f(f(1))=f(\sqrt {1+1})=f(\sqrt 2)=\sqrt {\sqrt 2+1}$
d) $(g\circ g)(0)=g(g(0))=g(3(0))=g(0)=3(0)=0$
