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

$\bullet\, 0<u<1,$

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

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

#HelpMe! #MathProblem

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Is there no one who can help me out with this problem ? Not even Calvin sir ?

Nishant Sharma - 8 years, 1 month ago

a nice problem you gave but sorry i could not solve it...hope anyone comes forward to confront this problem...:(

Sayan Chaudhuri - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$