Literally have no idea how to even start this question:

Prove that if f is continuous at $\displaystyle x_0$, then |f| is continuous at $\displaystyle x_0$.

Can someone give me a hint so I can start? Cheers.

Printable View

- Jan 22nd 2011, 02:40 AMworc3247Continuity Question
Literally have no idea how to even start this question:

Prove that if f is continuous at $\displaystyle x_0$, then |f| is continuous at $\displaystyle x_0$.

Can someone give me a hint so I can start? Cheers. - Jan 22nd 2011, 03:04 AMFernandoRevilla
Use:

$\displaystyle \left|\;|f(x)|-|f(a)|\;\right|\leq |f(x)-f(a)|<\epsilon$

Fernando Revilla