Answer
$a.\displaystyle \qquad\frac{11}{6}$
$b.\displaystyle \qquad\frac{3}{2}$
$c.\qquad 1$
$d.\displaystyle \qquad\frac{12}{17}$
Work Step by Step
$a.$
$(f\circ g)(4)=f[g(4)]$
$g(4)=\displaystyle \frac{3}{16+2}=\frac{3}{18}=\frac{1}{6}$
$f[g(4)]=f(\displaystyle \frac{1}{6})=|\frac{1}{6}-2|=\frac{11}{6}$
$b.$
$(g\circ f)(2)=g[f(2)] $
$f(2)=|2-2|=0$
$g[f(2)] =g(0)=\displaystyle \frac{3}{0+2}=\frac{3}{2}$
$c.$
$(f\circ f)(1) =f[f(1)]$
$f(1)=|1-2|=1$
$f[f(1)]=f(1)=1$
$d.$
$(g\circ g)(0)=g[g(0)]$
$g(0) =\displaystyle \frac{3}{0+2}=\frac{3}{2}$
$g[g(0)]=g(\displaystyle \frac{3}{2})=\frac{3}{\frac{9}{4}+2}=\frac{3}{\frac{17}{4}}=\frac{12}{17}$
