I got this question in a test of mine and it completely took me by surprise. I just can't "begin" to solve it.
Let a continuous function $f(x) : \mathbb R \rightarrow \mathbb R$ be defined such that it satisfies the relation $$f(x) + f(x + 2y) + 3xy = 2f(2y – x) + 2y^2 $$ for all $x, y\in R$. Comment whether the function is odd , into , one-one , and invertible.
I know what these terms necessarily mean in general , but I'm not sure how to check for them here.
I'm always having this general trend of getting troubled by functional equations and the ways of either deriving them or solving them. Apart from this question , it would be great help if anyone could suggest me some text or video where I could learn this topic better. ( The functional equations)