IMO Shortlist 2002 problem A1
Dodao/la:
arhiva2. travnja 2012. Find all functions
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
from the reals to the reals such that
for all real
![x,y](/media/m/f/b/6/fb60533620f22cd699e5b58ce9a646a4.png)
.
%V0
Find all functions $f$ from the reals to the reals such that
$$f\left(f(x)+y\right)=2x+f\left(f(y)-x\right)$$
for all real $x,y$.
Izvor: Međunarodna matematička olimpijada, shortlist 2002