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Re: Simple question about inverse of a function


f[t_] := (1 - t)^theta

InverseFunction[f][x] // Quiet

1 - x^(1/theta)

Plot3D[InverseFunction[f][x], {x, 0, 1}, {theta, 0, 5}] // Quiet


Bob Hanlon


On Sun, Oct 30, 2011 at 5:22 AM, Mikael <mikaen.anderson.1969 at gmail.com> 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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