       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)

```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

```

• Prev by Date: Re: Advice for writing small Scheme interpreter
• Next by Date: Re: Advice for writing small Scheme interpreter
• Previous by thread: Re: Applying a list of functions to a single number
• Next by thread: Re: Inverse of arbitrary functions