# Continuity Question

• Jan 22nd 2011, 03:40 AM
worc3247
Continuity Question
Literally have no idea how to even start this question:
Prove that if f is continuous at $x_0$, then |f| is continuous at $x_0$.

Can someone give me a hint so I can start? Cheers.
• Jan 22nd 2011, 04:04 AM
FernandoRevilla
Use:

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

Fernando Revilla