Re: Finding the inverse of a function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg24196] Re: [mg24193] Finding the inverse of a function?*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Fri, 30 Jun 2000 01:57:25 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

on 6/29/00 11:51 AM, heathw at in-tch.com at heathw at in-tch.com wrote: > Hi, > Is there some way to make Mathematica find the inverse of a user defined > function? I read the Mathematica Book and found InverseFunction[ ] but > it will only show the inverse of a Mathematica function. I would like to > be able to find the inverse of polynomials. > Thanks, > Heath > The only polynomials that have inverses are degree one polynomials, that is, non-constant linear functions. Of course if you only want a right inverse and do not care that it is not a continuous function of x in the complex plane, it is easy to do, e.g.: In[69]:= inverse[f_, x_] /; PolynomialQ[f, x] && Not[FreeQ[f, x]] := Module[{y}, Solve[f == y, x][[1, 1, 2]] /. y -> x] Now In[70]:= inverse[3x + 3, x] Out[70]= -3 + x ------ 3 In[71]:= inverse[3x^2 + 3x + 5, x] Out[71]= -3 - Sqrt[3] Sqrt[-17 + 4 x] ---------------------------- 6 In[73]:= 3x^2 + 3x + 5 /. x -> inverse[3x^2 + 3x + 5, x] // Simplify Out[73]= x or if you prefer In[74]:= Composition[3#^2 + 3# + 5 &, Function @@ {inverse[3#^2 + 3# + 5, #]}][ t] // Simplify Out[74]= t -- Andrzej Kozlowski Toyama International University, JAPAN For Mathematica related links and resources try: <http://www.sstreams.com/Mathematica/>