Re: Inverse Functions

*Subject*: [mg3211] Re: [mg3184] Inverse Functions*From*: richard at seuss.math.wright.edu (Richard Mercer)*Date*: 17 Feb 1996 23:03:03 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.*Sender*: daemon at wri.com

> 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. x^x is not one-to-one on (0,inf). A graph over the interval (0,1) clearly fails the horizontal line test. Even on a restricted interval where it is one-to-one, there is no reason to believe one can write a closed-form expression (i.e. elementary function) for the inverse. I strongly suspect that is not possible in this case. Richard Mercer