I'm having some problem with applying the inverse function theorem to prove this. Let $\displaystyle T(x): R^n \rightarrow R^n$ be a linear isomorphism, $\displaystyle f(x)=T(x)+h(x)$ such that $\displaystyle \mid{h(x)}\mid \leq M\mid x \mid^2$, and $\displaystyle f \in C^1(R^n,R^n)$. I want to show $\displaystyle f$ is invertible in neighborhood of $\displaystyle x=0$. Can someone help me with this?