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Homework Statement
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
Homework 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.
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?