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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
    
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
    
Sure, but the check mark is a very important piece of feedback. It's our (more tangible) way of knowing that the questioner found the answer given to be helpful. –  J. M. Nov 4 '11 at 10:26

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