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MathGroup Archive 1996

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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


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