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Re: finding inverses of functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126426] Re: finding inverses of functions
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Thu, 10 May 2012 04:55:41 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jod7lu$5f8$1@smc.vnet.net>

John Accardi wrote:

> Hello,  I am trying to get Mathematica to find the inverse of:
>
> y = 3x^3 + 2e^(2x)  (which I know is invertible)
>
> InverseFunction only seems to give inverses of built-ins, like Sine.
>
> I tried: 
>
> Solve[ y == 3x^3 + 2e^(2x), x ] but get a message that Solve does not have methods suitable.  (Solve works for simpler functions, however.)
>
> Any ideas?  Thanks.
>

Because your function is trancendental you can't hope for a closed form.
But InverseFunction can be used:

f[x_] = 3 x^3 + E^(2 x)
g[y_] = InverseFunction[f][y]

Plot[f[x], {x, -2, 3}]
Plot[g[y], {y, -50, 250}]

-- 
_________________________________________________________________
Peter Breitfeld | Bad Saulgau, Germany | http://www.pBreitfeld.de



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