A dominant and equivariant morphism has its image locally closed

Question

Please, I really appreciated if anybody can help me with this question or suggest a book:

I want to proof that:

Let $X,Y$ be two $G$-algebraic varieties and $f:X\rightarrow Y$ an equivariant and dominant morphism. If G is connected then $f(X)$ is open in $\overline{f(X)}$.

Thank you all!