You can compare the mean of the scaled values. I am computing the mean as it’s easy to compute.
u_your = (2*u_old - x_max)/(x_max)
whereas, u_minmax = (u_old - x_min)/(x_max - x_min)
you can see that the new means are going to be different after applying the scaling. Correspondingly you can also compute the variance to check if they differ.