# Math Help - Continuity of Functions

1. ## Continuity of Functions

In my analysis class we were discussing the continuity of various functions and my professor wrote some examples on the board. One being that if f is continuous then |f| is continuous, which I know is true but I couldn't complete the proof. Please help, this is driving me nuts.

2. It is trivial just note:
$\left| {\left| {f(x)} \right| - \left| {f(a)} \right|} \right| \le \left| {f(x) - f(a)} \right|
$
.

3. Originally Posted by Coda202
In my analysis class we were discussing the continuity of various functions and my professor wrote some examples on the board. One being that if f is continuous then |f| is continuous, which I know is true but I couldn't complete the proof. Please help, this is driving me nuts.
Hint: $||f(x)| - |f(x_0)|| < |f(x) - f(x_0)|$