Re: Inverse Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg3208] Re: Inverse Functions*From*: whitic at rpi.edu (whitic)*Date*: Sat, 17 Feb 1996 14:16:33 -0500*Organization*: Rensselaer Polytechnic Institute, Troy NY, USA*Sender*: owner-wri-mathgroup at wolfram.com

jcharko at microage-ll.awinc.com (Julian Charko) wrote: >As a relatively inexperienced user of Mathematica, could someone inform me >how to get a closed-form expression--in terms of elementary functions if >possible--for the inverse of the function > f(x) = x^x >Since the function is one-to-one over its domain, it does have a >mathematical inverse. >Thank You, >Julian P. Charko, P. Eng. What domain are you considering for this function? If you are taking the domain to be where the function is real valued, i.e. x>0, then this function is not one-to-one. By setting the derivative to zero you will find a stationary point at approx. x=.367879... and this is actually a minimum since the second derivative is > 0. If you are confining the function a the region where it is one-to-one, e.g. x>.5, then the inverse function theorem only says there exists an inverse, it doesn't say that it can be written in terms of elementary functions, and in this case it can not be. If you need to do this numerically on Mathematica, you could define a function such as: finv[f_,x1_,x2_] := FindRoot[ f-x^x==0, {x,x1,x2}] or something like this, where x1 and x2 is the interval where you expect to find x. Good luck Chris Whiting whitic at rpi.edu ==== [MESSAGE SEPARATOR] ====