(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A friend of mine tried to classify for the IMO a few days ago (he didn't do so well). A problem he had to solve was:

f(x + xy + f(y)) = (f(x) + 1/2)(f(x) + 1/2)

I didn't really understand what he said later. First he told me to find the values of X and Y for which this function makes sense, but later I asked him if it said anything more and he told me the domain and codomain were both R, which is a bit weird. As far as I know, the domain is all possible values of X.

2. Relevant equations

I probably misunderstood. I would appreciate it if anyone could tell me what it probably was, and, even better, tell me how to proceed.

3. The attempt at a solution

I got as far as f(x) = -1/2 +- f(x + xy + f(y)) using the quadratic formula... which checks out. My dad says I'm missing information. I don't really understand all this much.

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# Homework Help: Internat. Math Olympiad exercise. Weird function.

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