Let $F$ be any infinite field, $U\subset F^n$ be an open, dense (in Zariski topology) subset, $x_1,x_2,…,x_n$ be an algebraic independent system of variables over $F$ , $f,f_1,f_2,…,f_n \in F(x_1,x_2,…,x_n)$ be rational functions and $g:F^n\rightarrow F$ be a function(note that the rationality of the $g$ is not given). If $f(u)=g(f_1(u), f_2(u),…, f_n(u))$ for any $u\in U$ can one say that $f(x)\in F(f_1(x), f_2(x),…,f_n(x))$? In other words does it imply the "rationality" of $g$?