Let $\displaystyle f(x)=\frac{x}{1+|x|}$.

1. Show $\displaystyle f(x)$ is differentiable.

2. Find the inverse of $\displaystyle f(x)$.

3. Show $\displaystyle f^{-1}(x)$ is also differentiable.

I did (1). I have trouble finding the inverse of $\displaystyle f(x)$ so that it is differentiable. Some help please.