Answer
$a.\displaystyle \qquad\frac{1}{17}$
$b.\displaystyle \qquad\frac{1}{5}$
$c.\qquad 1$
$d.\displaystyle \qquad\frac{1}{2}$
Work Step by Step
$a.$
$(f\circ g)(4)=f[g(4)]$
$g(4)=\displaystyle \frac{1}{16+1}=\frac{1}{17}$
$f[g(4)]=f(\displaystyle \frac{1}{17})=|\frac{1}{17}|=\frac{1}{17}$
$b.$
$(g\circ f)(2)=g[f(2)] $
$f(2)=|2|=2$
$g[f(2)] =g(2)=\displaystyle \frac{1}{4+1}=\frac{1}{5}$
$c.$
$(f\circ f)(1) =f[f(1)]$
$f(1)=|1|=1$
$f[f(1)]=f(1)=1$
$d.$
$(g\circ g)(0)=g[g(0)]$
$g(0) =\displaystyle \frac{1}{0+1} =1$
$g[g(0)]=g(1)=\displaystyle \frac{1}{1+1}=\frac{1}{2}$