Polynomial joint pdf $f(x,y)$ such that of $f(x) \neq f(y)$

Question

How can I build a polynomial joint pdf $f(x,y)$ for $x \in [x_1, x_2]$ and $y \in [y_1, y_2]$ such that of $f(x) \neq f(y)$ or equivalently, $x$ and $y$ are depended on each other?

Answer 1

If you consider $$f(x,y)=\frac{2}{3}(x+2y){\bf 1}_{[0,1]\times[0,1]}(x,y)$$ then this will answer your question.