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MathGroup Archive 1996

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Re: Inverse Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3211] Re: [mg3184] Inverse Functions
  • From: Richard Mercer <richard at seuss.math.wright.edu>
  • Date: Sat, 17 Feb 1996 14:17:06 -0500
  • Sender: owner-wri-mathgroup at wolfram.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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