Calculating dew point and bubble point of gas mixtures
In the picture above, the C is the critical point. There seems to be some easy methods to calculate the critical temperature, but not so with the critical pressure.

For bubble point it would give me a good indication of where the max range is. 

But I realised that the critical temperature point won't help me finding the min and max range for dew point calculation. As you can see in the picture, the point M (max temperature point) would be a good indication of where the max range is for dew point.

Anyway I found a much simpler solution. I consider the bubble point and dew point calculation functions as a black box. 

As I'm only seeking the bubble point / dew point for a specified temperature, I step the possible pressure range (1 kPa - 10 MPa), with steps of 1 kPa. Then I calculate the numerical derivate of using current step and previous step. 

This function derivate is consistent and negative in the range of the function domain where a bubble or dew point value is valid.

Outside the function domain the derivate is close to zero (+-1E-15). 

So this gives me a good starting point for the root finding algorithm.

I also changed from False Position method to Bisection method, as it's less sensitive to derivates.

I hope this will help someone else with similar problem.