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Japan mathematical olympiad finals 2006, problem 3

Source:

March 3, 2006
functionLaTeXinductioncalculusderivativeratioalgebra

Problem Statement

Find all functions f,f, defined on real numbers and taking real values such that {f(x)}2+2yf(x)+f(y)=f(y+f(x))\left\{f(x)\right\}^2+2yf(x)+f(y)=f(y+f(x)) for all real numbers x,y.x,y.
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