Thursday, May 18, 2017

Functional equation extended solution

The question is Find all functions f:RR such that f(x+y)f(xy)=(f(x)+f(y))24x2f(y) Taking x=y=0, we get f(0)2=4f(0)2f(0)=0. Now take x=y which immediately gives 4f(x)2=4x2f(x)f(x)(f(x)x2)=0f(x)=0 or f(x)=x2 xR This was my solution. But I was stunned when I looked at the official solution.enter image description here




Why do we need to continue to do anything after getting what I got, isn't it sufficient?

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