I stumbled upon a theorem today that I feel like I’ve needed in the past, though I can’t remember any particular applications. I’m writing it up here as a note to my future self should the need reappear. The theorem gives sufficient conditions to conclude f(g(x)) ≤ g(f(x)) and uses this to prove, for example, […] The post f(g(x)) versus g(f(x)) first appeared on John D. Cook....