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Re: Simple question about inverse of a function


Inverse functions works on functions, not on the function evaluated at some point. So you want

f[t_] := (1 - t)^theta
finv = InverseFunction[f]
(* Returns: 1 - #1^(1/theta) & *)

InverseFunction does not check the possible branch structure of the function, so for non-built-in it gives the warning "Inverse functions are being used. Values may be lost for multivalued inverses."

You can check that things are ok using Reduce, or in your case

FullSimplify[f[finv[t]] == t, theta >= 1]
(* Returns: True *)



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