Let $f:\Omega\rightarrow R^n$ is $C^1$, $\Omega$ is bounded open subset of $R^n$.
And $f(x_0)=\theta$, $J_f(x_0)\ne 0$.$J_f$ is Jacobi of $f$, $\theta=(0,...,0)$.
Then ,how to show :
$f'(x_0)$ has bounded inverse.More detail, why $J_f(x_0)\ne 0$ make that $f'(x_0)$ has bounded inverse.
The more detail the better, thanks very much.
Sorry for my poor English.