Continuous Quotient

[Trumbone]

I'm looking for some help with proving that if f and g are continuous then so is f/g. I need to use the ? and ? definition of continuity
( ? x - a?< ? implies ?f(x) – f(a)?< ?) to prove this.

Thank you

 

[Deleted member 4993]

I'm looking for some help with proving that if f and g are continuous then so is f/g. I need to use the ? and ? definition of continuity
( ? x - a?< ? implies ?f(x) – f(a)?< ?) to prove this.

Thank you

We understand your needs - but we need to see:

Your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[daon]

In my opinion, its best to first show the property for products, then show, assuming f is nonzero and continuous at a then 1/f is also. Then you may use the product property with (g)(1/f)

 

[Trumbone]

Thank you Daon, I just want to make sure you indeed want to use g(1/f) and not f(1/g)?

 

[daon]

Thank you Daon, I just want to make sure you indeed want to use g(1/f) and not f(1/g)?

If you show it for an arbitrary continuous function the "letters" don't matter. If you prove that 1/f is continuous with the assumptions above, then if g also matches the hypothesis you may use 1/g.