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Let be a function $f(x)$ , I am interested in knowing a numerical nice method to get its functional inverse (assumed unique) $f(g(x))=x$.

Of course I know that I can reflect each point $(x,f(x)$ trough the line $y=x$ on the plane I know how to do it, but I was wondering if there are more effective method to get functional inverses.

Perhaps I could try with Newton method to solve the equation $y-f(x)=0$ and treat 'y' as a constant but I am not sure.. :(

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Yes, you can use Newton method (for a differentiable function) or other root-finding algorithms. –  hardmath Nov 3 '11 at 20:02
About two weeks ago, when you'd asked about half as many questions as you have now, I pointed out to you that you had accepted very few answers. You asked how to do this, and someone explained it. In the meantime, your accept rate has only decreased further. I suggest that you reflect on the possibility that very many of your questions are remaining unanswered because people disapprove of this uncooperative behaviour and are responding in kind. –  joriki Nov 3 '11 at 23:20
You can do a numeric solution for a given $y$, but that will only get you a numeric $x$. You could do this for a bunch of $y$ values and fit the resulting data to some functional form, perhaps suggested by the graph of the points. –  Ross Millikan Nov 4 '11 at 0:00
You might be able to use Lagrangian inversion of the series for $f(x)$ to obtain a series for the inverse. –  J. M. Nov 4 '11 at 0:55
but joriki i always give a 'thank you' to the people that helps me :) –  Jose Garcia Nov 4 '11 at 9:16

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