Answer
$a.\qquad\sqrt{13}$
$b.\qquad 3\sqrt{3}$
$c.\qquad\sqrt{\sqrt{2}+1}$
$d.\qquad 0$
Work Step by Step
$a.$
$(f\circ g)(4)=f[g(4)]$
$g(4)=3(4)=12$
$f[g(4)]=f(12)=\sqrt{12+1}=\sqrt{13}$
$b.$
$(g\circ f)(2)=g[f(2)] $
$f(2)=\sqrt{2+1}=\sqrt{3}$
$g[f(2)] =g(\sqrt{3})=3\sqrt{3}$
$c.$
$(f\circ f)(1) =f[f(1)]$
$f(1)=\sqrt{1+1}=\sqrt{2}$
$f[f(1)]=f(\sqrt{2})=\sqrt{\sqrt{2}+1}$
$d.$
$(g\circ g)(0)=g[g(0)]$
$g(0) =3(0) =0$
$g[g(0)]=g(0)=0$
