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Re: Simple question about inverse of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122521] Re: Simple question about inverse of a function
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 31 Oct 2011 06:48:57 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201110300922.EAA15359@smc.vnet.net>

InverseFunction will not work for functions defined by means of patterns 
and transformation rules. It works for pure functions as follows:


InverseFunction[Function[t, (1 - t)^theta]]
During evaluation of In[23]:= InverseFunction::ifun:Inverse functions 
are being used. Values may be lost for multivalued inverses. >>

Function[t, 1 - t^(1/theta)]

Using Assuming is useless here (and in any case, Assuming is useless 
unless used with functions such as Simplify, FullSimplify and some 
others). There is no way to give a domain specification to Function, 
hence there is no way to avoid the warning message (unless you choose to 
turn it off).

In fact, InverseFunction simply uses Solve in such cases so it only 
saves you some typing...


Andrzej Kozlowski


On 30 Oct 2011, at 10:22, Mikael wrote:

> I have a simple question on how to calculate the inverse of a a
function. This is the function I define:
>
> f[t_] := (1 - t)^theta
>
> To calculate the inverse I write:
>
> Assuming[t >= 0 && t <= 1 && theta >= 1 && theta < Infinity, { 
InverseFunction[f[t]]}]
>
> but the answer I get is
>
> {InverseFunction[(1 - t)^theta]}.
>
> Now I know I can do this:
>
> In[11]:= Solve[f[g[x]]==x,g[x]]
> Out[11]= {{g[x]->1-x^(1/theta)}}
>
> but I wonder what is the correct way of specifying assumptions on t 
and theta to make the InverseFunction work. Thanks.
>




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