This says that the way that growing the input by a factor of x changes the output is exactly the opposite from the way that shrinking the input by a factor of x changes the output\. In terms of the "communication cost" interpretation, if doubling \(or tripling, or n\-times\-ing\) the possibility space increases costs by c, then halving \(or thirding, or n\-parts\-ing\) the space decreases costs by c.
May need to build the intuition that knowing how f(x) behaves tells me how f(c*x) is different from f(c).
(You're using the language of "growing the input," but I just see a static input called x.)