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.