How do i deal with stuff like that? tried to just write many equalities but it just doesnt help... The equation is $f(x^2+y)=f(x)+f(y^2)$.
EDIT: the question is to find all functions such that this equation holds for them. From real to real.
You can solve this pretty immediately by looking at the cases $x=0$, $y=0$, and $x^2+y=0$. (The only possibility is the constant zero function.)
I would try to see how it behaves at "special points" like +-1, 0 and some others, and see how it can behave.
For example, if you let $y=0$ this becomes $f(x^2) = f(x)$.
Then for $x=y=1$ you get $f(2) = 2f(1)$.
For $x=1, y=-1$ you get $f(0) = 2f(1)$ also...
Try a few more combinations and you'll get enough constraints to define $f$, or reach a contradiction.