#### Answer

(a) $\dfrac{1}{17}$
(b) $\dfrac{1}{5}$
(c) $1$
(d) $\dfrac{1}{2}$

#### Work Step by Step

(a) $(f\circ g)(4)= f(g(4))=f\left(\dfrac{1}{4^{2}+1}\right)=f\left(\dfrac{1}{17}\right)=\left|\dfrac{1}{17}\right|=\dfrac{1}{17}$
(b) $(g\circ f)(2)=g(f(2))=g(|2|)=g(2)=\dfrac{1}{2^{2}+1}=\dfrac{1}{5}$
(c) $(f\circ f)(1)=f(f(1))=f(|1|)=f(1)=|1|=1$
(d) $(g\circ g)(0)=g(g(0))=g\left(\dfrac{1}{0^{2}+1}\right)=g(1)=\dfrac{1}{1^{2}+1}=\dfrac{1}{2}$