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INMO coming! "Functional equation"

Find all functions \[f:\mathbb{R}\rightarrow \mathbb{R}\] \[f(xf(y)+f(x))=2f(x)+xy\] for all real \(x\) and \(y\).

Note by Aaron Jerry Ninan
10 months, 2 weeks ago

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@Harsh Shrivastava- Yes. For the question, how will one prove that there doesnt exist any function other than f(x)=x+1.

Aaron Jerry Ninan - 10 months, 2 weeks ago

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What have you tried? Where are you stuck?

Calvin Lin Staff - 10 months, 2 weeks ago

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I got one function f(x)=x+1 .I want to know if there exist any other functions satisfying the equation ,if not,how to prove it. I assumed that f(x)>x+1 in one case and f(x)<x+1 in other case. In both cases i am not able contradict something but instead i am getting some conditions on x,y...etc. Please help.

Aaron Jerry Ninan - 10 months, 1 week ago

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@Aaron Jerry Ninan @Calvin Lin- please reply

Aaron Jerry Ninan - 10 months, 1 week ago

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@Sharky Kesa @Priyanshu Mishra Please share your solutions

Aaron Jerry Ninan - 10 months, 2 weeks ago

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Did you came to rmo camp held in Bhilai ?

Harsh Shrivastava - 10 months, 2 weeks ago

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Did you solve the last geometry question given in our practice paper(1). i think the question is wrong since BDC is a straight line and 3x doesnt make sense.

Aaron Jerry Ninan - 10 months, 2 weeks ago

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