# Math Help - Limit Proof

1. ## Limit Proof

Let g be defined on the Reals by g(1) = 0, and g(x) = 2 for all x not equal to 1. Let f(x) = x + 1 for all x in the Reals. Show that lim(as x->0) of g(f(x)) does not equal g(f(0)).

I don't know how to go about proving this, so any help is much appreciated. Thanks!

2. Originally Posted by jkru
Let g be defined on the Reals by g(1) = 0, and g(x) = 2 for all x not equal to 1. Let f(x) = x + 1 for all x in the Reals. Show that lim(as x->0) of g(f(x)) does not equal g(f(0)).

I don't know how to go about proving this, so any help is much appreciated. Thanks!
Simply notice that as $x\to{0^\pm}$ you have that $f(x)\to{1^{\pm}}$ so $g(f(x))\to{2}\ne{g(f(0))=1}$