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Math Help - Continuity of Functions

  1. #1
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    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.
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    It is trivial just note:
    \left| {\left| {f(x)} \right| - \left| {f(a)} \right|} \right| \le \left| {f(x) - f(a)} \right|<br />
.
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  3. #3
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    Quote Originally Posted by Coda202 View Post
    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)|
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