Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises - Page 44: 52

$h(x)=|x|$ $g(x)=2+x$ $f(x)=\sqrt[8] x$

Separating the function into three processes: $1. h(x)=|x|$ $2. g(h(x))=g(|x|)=2+|x|=2+h(x)$ $g(x)=2+x$ $3. f(g(h(x)))=f(2+|x|)=\sqrt[8] {2+|x|}=\sqrt[8] {g(h(x))}$ $f(x)=\sqrt[8] x$