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Re: finding inverses of functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126427] Re: finding inverses of functions
  • From: A Retey <awnl at gmx-topmail.de>
  • Date: Thu, 10 May 2012 04:56:02 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jod7lu$5f8$1@smc.vnet.net>

Am 09.05.2012 09:51, schrieb John Accardi:
> Hello,  I am trying to get Mathematica to find the inverse of:
>
> y  = 3x^3 + 2e^(2x)  (which I know is invertible)

but do you know a symbolic solution? I think solving equations of this 
type symbolically is difficult, if not impossible in general.

> InverseFunction only seems to give inverses of built-ins, like Sine.

InverseFunction works as designed for your case, it just doesn't provide 
a simple symbolic expression. But this works as expected:

finv = InverseFunction[3 #^3 + 2 E^(2 #) &]

Plot[finv[x], {x, -10, 10}]

note that the InverseFunction object represents the inverse function 
without the need to actually be able to determine a symbolic expression 
in general. It can be used like any other function definition in most 
functions that work with functions and they will return values when 
given arguments. The same is true for InterpolatingFunction and 
CompiledFunction objects.

In this case InverseFunction returns Root objects for exact numbers 
(e.g. finv[1]) and floating point approximations for floating point 
arguments (e.g. finv[1.]). Probably that's the best a computer program 
can do for a general case like this. TI consider this the true power of 
Mathematica :-)

hth,

albert



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