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Functional Equations Discussion/Forum

Lets make a "forum" like thing for "Functional Equations".

I will post a question here, the person who solves it, would post another question and so on.

Lets make it short and simple :)

Question 1: Find all the functions $$f\colon\mathbb{Q} \to \mathbb{Q}$$ such that $f(x+y) + f(x-y) = 2f(x) + 2f(y)$ for all rationals $$x,y$$.

Note: The answer showed be accompanied with a valid proof.

Note by Aditya Agarwal
1 year ago

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There is already a Fuctional Equations Contest going on. But I think that the contest is currently paused as there are three other contests going on currently. · 1 year ago

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