AS/A2 Pure 4 Pure 6

P5 Topic 2: Hyperbolic functions
Graphs and properties: arc cosh(ax)
Move the point a left or right to change the value of the parameter a in the graph of y = arccosh(ax). Also displayed are the inverse function and the line y=x. What is the equation of the inverse function?

Summary the graphs of y = arccosh(ax) and its inverse function are reflections in the line y=x arccosh(ax) is not a 1-1 function, but arccosh(ax), for positive x is, therefore the inverse function only applies to this positive part the equation of the inverse function is y=(cosh x)/a The Plane Graphic Calculator java applet