Given sinhx = 0.5(e^x - e^-x), express its inverse, arcsinhx in terms of x.

The first step is to write sinhx in its exponential form and set it equal to y, this will make rearranging easier. Then multiply everything by e^x and rearrange to form a quadratic, in terms of e^x. Express e^x using the quadratic formula and from here rearrange to find x in terms of y. This can then be used to find arcsinhx in terms of x, as sinhx = y and x = arcsinhy.