Let .
1. Show is differentiable.
2. Find the inverse of .
3. Show is also differentiable.
I did (1). I have trouble finding the inverse of so that it is differentiable. Some help please.
The first thing I'd do is draw a graph of y = f(x).
Note that if and if .
Clearly the domain of y = f(x) is all real numbers and the range is (-1, 1).
Use the above to inform your thinking on the inverse function and its differentiability. In particular, what's the domain of