Question

If f(x) = |x|, prove that fof = f.

Answer 1

Domains of f and fof are same as R.
$$\begin{gathered} \left(fof\right)\left(x\right)=f\left(f\left(x\right)\right)=f\left(\left|x\right|\right)=\left|\left|x\right|\right|=\left|x\right|=f\left(x\right) \\ \text{So,} \\ \left(fof\right)\left(x\right)=f\left(x\right),\forall x\in R \\ \text{Hence,}fof=f \end{gathered}$$