find all functions such that : for every x ,y in R
f(x)+f(y)=f(x+f(y))
Interesting question. Is there any context? For example are these linear functions? Or all functions?
would be one, for all (this includes the identity function), as would the zero function, .
Now, if the question was about linear bijections then there is only one such function, which would be a nice question. However, this question is much too vague. I mean, the function,
is a function of this form. And it's hideous.