On Wed, 01 Jun 2011 12:35:03 -0700, Alexandros Bantis <email@example.com> wrote in <news:94nij9F5phU1@mid.individual.net> in alt.math.undergrad:
> I'm curious. How is it possible that the function changes > a fundamental property [f(5) == undefined versus f(5) = > 1/6] when all I've done is multiply by 1. I see that > this has happened, but intuitively it feels odd.
It didn't change when you multiplied by 1: the change occurred when you cancelled x - 5. After the multiplication by 1 you actually had
(x - 5) / [(x - 5) sqrt(x + 4) + 3],
which is exactly equal to f and in particular undefined at x = 5. In other words,