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MathNet 2014 Question 11

Math Olympiad Vault · MathNet 2014

Question 11

Find all functions $f : \mathbb{R}^+ \to \mathbb{R}^+$ such that for all positive real numbers $x$ and $y$,
$$
f\left(\frac{y}{f(x+1)}\right) + f\left(\frac{x+1}{x f(y)}\right) = f(y).
$$