If $\phi : M = \mathbb{R}^n \setminus \{0\} \to \mathbb{R}^n$ is defined by $\phi(x) = x + \frac{x}{|x|}$, find $\phi^{-1}$ 
If $\phi : M = \mathbb{R}^n \setminus \{0\} \to \phi[M] \subseteq \mathbb{R}^n$ is defined by $\phi(x) = x + \frac{x}{|x|}$, find $\phi^{-1}$

I'm not sure how to go about finding $\phi^{-1}$ here. $\phi$ is clearly injective, and bijective on $M$, so $\phi^{-1}$ must exist, but I'm not entirely sure how to go about algebraically finding the inverse $\phi^{-1}(x)$. 
How can I go about doing so? If it helps the boundary of $\phi[M]$ is $S^{n-1}$.

Hint :
$\phi$ takes a point $x$, and extends it by a unit length of $x$. Thus the inverse $\phi^{-1}$ is such that it takes a point and remove that extension.
