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.
