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Inverse of arbitrary functions

• To: mathgroup at smc.vnet.net
• Subject: [mg74497] Inverse of arbitrary functions
• From: Dave Rudolf <dave.rudolf at usask.ca>
• Date: Fri, 23 Mar 2007 19:06:35 -0500 (EST)
• Organization: University of Saskatchewan

Hey all,

Is there some way to get Mathematica to find the symbolic inverse of a 
user-defined function? I know that I can use InverseFunction to find the 
inverse of simple functions, like so:

	InverseFunction[Log] -> Exp

However, I would like to do something like

	f[ x_ ] = x + sin[ x + cos[ x ] ]

	InverseFunction[ f ]

I did run across a similar newsgroup post that said to use the Solve 
function, like so:

	inverse[f_, x_] /; PolynomialQ[f, x] && Not[FreeQ[f, x]] :=
		 Module[{y}, Solve[f == y, x][[1, 1, 2]] /. y -> x]

However, it doesn't seem to work as is, and I don't understand the 
syntax of some of the stuff. Like, what's with the -> symbol? And \; for 
that matter?

Anyway, let me know if there is some other way to pull this off.

Thanks.

Dave

• Follow-Ups:
  • Re: Inverse of arbitrary functions
    • From: "Chris Chiasson" <chris@chiasson.name>