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MathGroup Archive 2001

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Re: inverse function computation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31689] Re: [mg31660] inverse function computation
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Sat, 24 Nov 2001 16:44:04 -0500 (EST)
  • References: <200111231046.FAA24056@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Margot wrote:
> 
> Hello,
> 
> I'd like to do the following manipulation.
> Let f be a homeomorphism (known explicitly).
> I want Mathematica to compute its inverse f^{-1} and to use it
> for further computations and plots.
> I'm assuming here that f^{-1} is not explicit (take f(x)=x+0.2Sin[x] for
> instance).
> 
> I'm not sure that Mathematica has an already built-in function; do you know
> any simple algorithm?
> 
> Many thanks

You could do this with explicit inversion via root-finding. One approach
might be as below.

numInvert[f_][y_?NumberQ] := Module[{x}, x /. FindRoot[y==f[x], {x,0}]]

For your example you could do

f[x_] = x+0.2*Sin[x]

Plot[numInvert[f][y], {y,0,1}]


Daniel Lichtblau
Wolfram Research


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