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f (f (f (k))) = k if f (n) =n + 3 for n odd , f(n) = n/2 for n rvrn

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist F1 day1 (F= functions)

September 29, 2021
algebrafunction

Problem Statement

A function ff defined on integers such that
f(n)=n+3f (n) =n + 3 if nn is odd f(n)=n2f (n) = \frac{n}{2} if nn is even
If kk is an odd integer, determine the values for which f(f(f(k)))=kf (f (f (k))) = k.
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