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Re: Simple question about inverse of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg122538] Re: Simple question about inverse of a function
• From: Simon <simonjtyler at gmail.com>
• Date: Mon, 31 Oct 2011 06:52:02 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j8j5ci$f6v$1@smc.vnet.net>
• Reply-to: comp.soft-sys.math.mathematica at googlegroups.com

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 *)