The bivariate function from its marginals

Question

Suppose I have a bivariate function, $f(x,y)$. Fixing $x$, we define $f_x(y)=f(x,y)$. Fixing $y$, we define $f_y(x)=f(x,y)$. Now if we know the form of $f_x(.)$ for all $x$, and the form of $f_y(.)$ for all $y$, is there any method to derive the form of $f(x,y)$?

Answer 1

Yes, if you have $f_x$ for all x you have a function $g: x \mapsto f_x$ and $f(x,y) = g(x)(y)$. Does this help you? Otherwise make clear what you mean by "the form".