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Re: Inverse Functions

• Subject: [mg3239] Re: Inverse Functions
• From: john at janacek.demon.co.uk (John Tanner)
• Date: 19 Feb 1996 07:42:40 -0600
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.
• Sender: daemon at wri.com

In article <4fpdob$f9r at dragonfly.wolfram.com>, Julian Charko
<jcharko at microage-ll.awinc.com> writes
>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.
>
>
>

Because all variables are assumed as complex, there are inherently
multiple solutions: for example x=I and x=-I.

However, even for real cases there are multiple solutions: for example
x=0 and x=1 (and points in between).

I wish you luck in trying to disentangle this: you may get a specific
solution for a given range but there seems not to be a general solution.
More info required: you have our interest.

--
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I really ought to sell it     :  home -  john at janacek.demon.co.uk
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but only what I tell it.      :  work -  john.tanner at gecm.com