Question:
If $f(x)=|x|$, prove that $f \circ f=f$
Solution:
Domains of f and fof are same as R.
$(f o f)(x)=f(f(x))=f(|x|)=|| x||=|x|=f(x)$
So,
$(f o f)(x)=f(x), \forall x \in R$
Hence, $f o f=f$
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