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Simple question about inverse of a function


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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