Question

For \[f(x)=|1-x+|x||\], which functions give the representation \[f(x)=h(g(x))\]?

Options

• \[g(x)=1-x+|x|\] and \[h(x)=|x|\]

• \[g(x)=|x|\] and \[h(x)=1-x+|x|\]

• \[g(x)=1-x\] and \[h(x)=x^2\]

• \[g(x)=\sin x\] and \[h(x)=x^2\]

Answer 1

The inner expression inside the outer absolute value is \[g(x)=1-x+|x|\]. Applying \[h(x)=|x|\] to this inner value gives \[h(g(x))=|1-x+|x||\].