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

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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