Simple math question

[TecHNooB]

Been confusing myself over this issue for a while. If I have a function X(f) and I have an rectangle wave that goes from -1/2 to 1/2 (ignore magnitude, doesn't matter) on a frequency axis, what would the points be on the w axis (w = 2*pi*f). Initially, I thought it was -pi to pi on the w axis, but by definition, X(W) = X(2*pi*f) which implies that X(W) is equal to X(f) scrunched by 2*pi and so the result may be -1/(4*pi) to 1/(4*pi) on the w axis. I'm confusing myself here over a simple concept.