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

InterviewSolution

1.

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

Answer»

Given that f(x) = |x|,

Let us prove that fof = f.

Consider that (fof)(x) = f(f(x))

= f(|x|)

= ||x||

= |x|

= f(x)

Therefore, (fof)(x) = f(x), ∀ x ∈ R

Hence, fof = f

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