(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Okay, so if f and g are continuous functions at a, then prove that f/g is continuous at a if and only if g(a) # 0

2. Relevant equations

Assuming to start off the g(a)#0, by the delta-epsilon definition of continuity, basically, We know that |f(x)| and |g(x)| are bounded.

3. The attempt at a solution

I have messed around with the end result that we need, which is when |x-a|< delta

|f(x)/g(x)-f(a)g(a)|<Epsilon. This is what I've come up with:

|1/(g(x)g(a))|*|f(x)g(a)-f(a)g(x)|.

By looking at each piece it seems like they can be bounded as well. However, how do i manipulate what each one is bounded by so that when I multiply and add everything out, I get a nice simple Epsilon?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving division of continuous functions

**Physics Forums | Science Articles, Homework Help, Discussion**