$DF(x)$ is invertible. Then is there exists $G:F(R^n) \to R^n$ such that $G(F(x))=x$??

Question

$F:R^n \to R^n$ be continuously differentiable function.

If $DF(x)$ is invertible for every $x \in R^n$. Then there exists $G:F(R^n) \to R^n$ such that $G(F(x))=x$??

Prove or disprove.