Answer
$a.\qquad 4418$
$b.\qquad-191$
$c.\qquad 8$
$d.\qquad-2$
Work Step by Step
$a.$
$(f\circ g)(4)=f[g(4)]$
$g(4)=1-3(4^{2})=1-3(16)=-47$
$f[g(4)]=f(-47)=2(-47)^{2}=4418$
$b.$
$(g\circ f)(2)=g[f(2)]$
$f(2)=2(2)^{2}=8$
$g[f(2)]=g(8)=1-3(8)^{2}$
$=1-3(64)=-191$
$c.$
$(f\circ f)(1)=f[f(1)]$
$f(1)=2(1)^{2}=2$
$f[f(1)]=f(2)=2(2)^{2}=8$
$d.$
$(g\circ g)(0)=g[g(0)]$
$g(0)=1-3(0)^{2}=1$
$g[g(0)]=g(1)=1-3(1)^{2}=-2$
