That is, the inverse of (e^x - e^-x) / 2. The answer is x + sqrt(x^2 + 1). If you start with x = (e^y - e^-y ) / 2, what intermediary steps lead to the answer?

You can clear the denominator:

2x = e^y - e^-y;

you can re-write e^-y as 1/e^y:

2x = e^y - 1/e^y;

you can then clear that denominator:

2xe^y = e^2y - 1;

I'm basically out of ideas at this point. Hmm term on the right is a difference of two squares. I would appreciate any comments!