i know sinh(x) = (e^x - e^-x)/2
but what is sinhInverse(x) equal to?
First of all, the terminology is "hyperbolic" not "hyperbole."
We have a function
To find the inverse we need to switch the roles of x and y:
and solve for y:
<-- Multiply through by
This is a quadratic in , so
We discard the "-" solution since the arguement of ln cannot be negative. ( is negative everywhere.)
So finally
This is the inverse function to sinh(x). (The dotted line in the graph below is the line y = x.)
-Dan