Butters, Without additional conditions, I don't think it's true. Let A and B both denote the nonnegative real numbers. Define f mapping A to B by f(x) = sqrt(x), where "sqrt" denotes the square root. Now if x < y, f(x) - f(y) is not in B. Hope this helps. Ben
> Date: Thu, 5 Apr 2012 07:50:10 -0400 > From: email@example.com > To: firstname.lastname@example.org > Subject: Functions need Help > > Let f : A ? B be a function, with S, T ? A. Show that f[S] ? f[T] ? f[S ? T]. Give an example where equality fails. > > I dont understand how to start this.