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Re: Simple question about inverse of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122593] Re: Simple question about inverse of a function
  • From: Mikael <mikaen.anderson.1969 at gmail.com>
  • Date: Wed, 2 Nov 2011 06:23:33 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

> Hi,
> 
> > 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.
> >
> It has nothing to do with the assumptions, you just
> should not specify 
> the argument. This will do what you want:
> 
> finv = InverseFunction[f]
> 
> it will warn about multivalued inverses, and I don't
> think you can avoid 
> that warning with appropriate assumptions for theta
> in that case. Of 
> course you can use Quiet to suppress it, but then you
> should be sure 
> that everything is alright for your use cases...
> 
> hth,
> 
> albert
> 

Many thanks to Albert and Simon for explaining the problem.



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