Higher Secondary 2011

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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asif e elahi
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Higher Secondary 2011

Unread post by asif e elahi » Mon Jan 13, 2014 4:45 pm

Let $f$ be an injective function and $f: \mathbb R^{+} \mapsto \mathbb R^{+}$. $f(1)=2$ and $f(x+\frac{1}{f(y)})=\frac{f(x)f(y)}{f(x)+f(y)}$ for all positive real $x$ and $y$. Find $f(2012)$.

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*Mahi*
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Re: Higher Secondary 2011

Unread post by *Mahi* » Tue Jan 14, 2014 3:30 pm

Outline:
Use $f$ injective and some algebraic manipulation to get $x+ \frac 1 {f(y)} = y+ \frac 1 {f(x)}$, and from there, use $\frac 1 {f(n+1)} - \frac 1 {f(n)} = 1$ to find $f(2012)$.
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Labib
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Re: Higher Secondary 2011

Unread post by Labib » Tue Jan 14, 2014 4:19 pm

I think this post should be in Divisional Olympiad forum. Was this posted before?
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