If a given f(x) function have several real or complex roots where its value is zero , one of the most used method to recover that roots is the Newt Raphson method . For a given starting point x0 , if the function f(x) is a proper one the x0 converge to a list of point with the final convergent point is a zero of f(x). My question is :

If i have a general Map that have one or several Fixed Point it is possible to think that exist an f(x) associated ? Is this f(x) unique or there is a family of them.

• Remember For NR Method that the Map is : G(x) = x - f(x)/diff(f(x),x) but it is possible to recover f(x) from G(x) using the derivative of ln(f(x)) .
• Then thank to this inversion map we have the f(x) associated to G(x) but the division of f and its derivativ can hide some common factor .

HAve you experience on this?? I am not a Math expert but Engineer User of Math. Thank you.