Why is y = f(2x) actually x variable divided by 1/2 in horizontal stretching/compression?

Say you have a point (a, b) on f(x), for the same function value to be on f(2x) you need the argument of the function to be the same as before, this means that the point is now (a / 2, b). We say that the function has been compressed in the x direction, since the same function value is reached with a smaller x value.