Is 1/f(x) Continuous at c if f is Continuous and Non-Zero?

[gonzo55]

Homework Statement

using the epsilon delta definition of continuity prove that if f is continuous at c with F(c)/=0 then 1/f(x) is also continuous at c.

Homework Equations

i don't know how to begin using the definition. I am just really struggling with this. Just need a place to start.

The Attempt at a Solution

do you use the definition like 1/fx -1/fc <e when x-c< delta?

 

[lanedance]

so what is the epsilon delta definition of continuity?

start with what you know about f and what you want to show about 1/f