find the domain of a function, given the root of it

Question

I need help writing a method that receives a function, and some number y and returns x such that f(x) = y. The function is differentiable using Newton's method:

from random import *

def diff_param(f,h=0.001):
    return (lambda x: (f(x+h)-f(x))/h)


def NR(func, deriv, epsilon=10**(-8), n=100, x0=None):
""" returns a number such that f(number) == 0"""
    if x0 is None:
        x0 = uniform(-100.,100.)
    x=x0; y=func(x)
    for i in range(n):
        if abs(y)<epsilon:
            #print (x,y,"convergence in",i, "iterations")
            return x
        elif abs(deriv(x))<epsilon:
            #print ("zero derivative, x0=",x0," i=",i, " xi=", x)
            return None
        else:
            #print(x,y)
            x = x- func(x)/deriv(x)
            y = func(x)
    #print("no convergence, x0=",x0," i=",i, " xi=", x)
    return None

I need to write a method source(f,y) that returns the x such that f(x) = y.

def source(f,y):

Answer 1

You need to find the zeros of g(x) = f(x)-y :

def source(f,y):
    def g(x):
         return f(x)-y
    x = NR(g, diff_param(g))
    return x

This returns a single x, but there may be others. To find them you need to try other initial values x0.