Can someone prove this following question with the given hint?

47.9" Let f(x, y) be a function from R into R such that for each xeR, f() =f(x,y) is a poly- nomial of finite degree in y (the degree dependent only on x). Also for each JER, f,(x) =/(x,>) is a polynomial of finite degree in x (the degree dependent only on y). Prove that f(x, y) is a finite polynomial in x and y, that is,R = Uo X = UR=.Ym implies * + 0 + If for some integers k and I by the Baire category theorem