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!