## Precalculus (10th Edition)

a) $\dfrac{1}{17}$; b) $\dfrac{1}{5}$; c) $1$; d) $\dfrac{1}{2}$
We are given the functions: $f(x)=|x|$ $g(x)=\dfrac{1}{x^2+1}$ 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) $(g\circ g)(0)=g(g(0))=g\left(\dfrac{1}{0^2+1}\right)=g(1)=\dfrac{1}{1^2+1}=\dfrac{1}{2}$