InverseFunction: how to manage?

*To*: mathgroup at smc.vnet.net*Subject*: [mg124268] InverseFunction: how to manage?*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Sat, 14 Jan 2012 17:17:21 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I apologize for asking this very elementary question but how do I manage InverseFunction? Here is an example When I solve the equation of motion for a pendulum f''[t] == Cos[f[t]], f[0]== 0, f'[0] == 0 I get (with paper and pencil) the time t as a function of the angle f thus t[f_] = Integrate[1/Sqrt[Sin[u]], {u, 0, f}] Out[22]= 2*(EllipticF[f/2 - Pi/4, 2] + EllipticF[Pi/4, 2]) Now I want the the angle as a function of time (f[t]) like this "f[t_] = InverseFunction[t[f]]" But this does not work. I also tried to define t as a pure function t = 2*(EllipticF[#1/2 - Pi/4, 2] + EllipticF[Pi/4, 2]) & but again, I have not seen a way to invert this, and for instance carry out Plot[f,{t,0,2 Pi}]. Thanks in advance for any hints. Best regards, Wolfgang

**Follow-Ups**:**Re: InverseFunction: how to manage?***From:*Murray Eisenberg <murray@math.umass.edu>