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Re: Re: InverseFunction[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41971] Re: [mg41950] Re: InverseFunction[]
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Wed, 11 Jun 2003 13:18:15 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <bbt23g$nj3$1@smc.vnet.net> <bc1jh1$bjp$1@smc.vnet.net> <200306110749.DAA02507@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

What does "knows about" mean in your answer?  Evidently Mathematica 
knows a NAME (ProductLog) for the inverse function and can evaluate it 
numerically.  But what is the definition of the function as Mathematica 
knows it?

Paul Abbott wrote:
> In article <bc1jh1$bjp$1 at smc.vnet.net>,
>  wself at msubillings.edu (Will Self) wrote:
> 
> 
>>You can easily write down a function which has an inverse, but the
>>inverse cannot be expressed in closed form, or in symbols that anyone
>>has invented.  For example, f[x_]= x*E^x.  This function is increasing
>>on (for example) the interval [1,3], therefore an inverse exists, at
>>least for 1 <= x <= 3.  But (as far as I know) this inverse function
>>has no name.
> 
> 
> Your point is valid. However, try Solve[x*E^x == y, x] and you'll see 
> Mathematica knows about the inverse function for your example.
> 
> Cheers,
> Paul
> 

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Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
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University of Massachusetts                413 545-2859 (W)
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