The discussion revolves around finding all functions \( f: \mathbb{R} \to \mathbb{R} \) that satisfy the equation \( f(x) + f(y^2) = f(x^2 + y) \) for all \( x, y \in \mathbb{R} \). Participants are exploring the nature of this functional equation and the definitions involved.
The discussion is ongoing, with participants providing guidance on testing specific cases and seeking clarification on the problem's setup. There is no explicit consensus yet, but some productive lines of questioning and exploration are evident.
Participants note potential language barriers and the original poster's unfamiliarity with the problem, indicating a need for clearer communication and support.
Pere Callahan said:Is your question to find all functions [itex]f:\mathbb{R}\times \mathbb{R}\to\mathbb{R}[/itex] such that [itex]f(x)+f(y^2)=f(x^2+y)\quad\forall x,y \in \mathbb{R}[/itex]?
If you want us to help you, show some effort. What have you tried so far?
Pere Callahan said:Is the function defined on R or on RxR...?
Take some special values for x and y, like x=0, or y=0 or x=y and see where it takes you.
Pere Callahan said:Sorry, I do not understand what you are saying. I suggest you try and find someone to help you who speaks your language.