Prove that

Question:

Let $f: R \rightarrow R: f(x)=|x|$, prove that $f$ o $f=f$.

Solution:

To prove: f o f = f

Formula used: f o f = f(f(x))

Given: (i) f : R → R : f(x) = |x|

Solution: We have,

$f \circ f=f(f(x))=f(|x|)=|| x||=|x|=f(x)$

Clearly $f$ o $f=f$

Hence Proved.