Inverse of a function using binary search

inverse.py

def inverse(x, f, k = 15):
  beg = 0
  end = 1
  while f(end) < x:
    beg += 1
    end += 1
  while k:
    mid = (beg + end) / 2
    if f(mid) > x:
      end = mid
    else:
      beg = mid
    k -= 1
  return beg

lambert = lambda y: y * (2.71828 ** y)
x = 3
res = inverse(x, lambert)
print(f"f({res:.5f}) = {lambert(res):.5f} != {x}")