Answer
$a.\qquad 97$
$b.\displaystyle \qquad-\frac{163}{2}$
$c.\qquad 1$
$d.\displaystyle \qquad-\frac{3}{2}$
Work Step by Step
$a.$
$(f\circ g)(4)=f[g(4)]$
$g(4)=3-\displaystyle \frac{1}{2}(4^{2})=3-8=-5$
$f[g(4)]=f(-5)=4(-5)^{2}-3$
$=4(25)-3=100-3=97$
$b.$
$(g\circ f)(2)=g[f(2)]$
$f(2)=4(2)^{2}-3=4(4)-3=16-3=13$
$g[f(2)]g(13)=3-\displaystyle \frac{1}{2}(13)^{2}$
$=3-\displaystyle \frac{169}{2}=-\frac{163}{2}$
$c.$
$(f\circ f)(1)=f[f(1)]$
$f(1)=4(1)^{2}-3=4(1)-3=4-3=1$
$f[f(1)]=f(1)=1$
$d.$
$(g\circ g)(0)=g[g(0)]$
$g(0)=3-\displaystyle \frac{1}{2}(0)^{2}=3-0=3$
$g[g(0)]=g(3)=3-\displaystyle \frac{1}{2}(3)^{2}=3-\frac{9}{2}=-\frac{3}{2}$
