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Problem on functions

Guys please help me solve this problem(it is troubling me).......

Let f:R+ --> R be defined as f(x)=x + (1/x) -\(\lfloor\) x + (1/x) \(\rfloor\). It is required to prove that there are infintely many rational numbers u so that

\(\bullet\, 0<u<1, \)

\(\bullet\, u,\,f(u),\, f(f(u)) \:are\: all\: distinct,\: and \)

\(\bullet\, f(f(u))= \,f(f(f(u))) \)

Note by Nishant Sharma
4 years, 3 months ago

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a nice problem you gave but sorry i could not solve it...hope anyone comes forward to confront this problem...:( Raja Metronetizen · 4 years, 3 months ago

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Is there no one who can help me out with this problem ? Not even Calvin sir ? Nishant Sharma · 4 years, 3 months ago

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