Absolute Value and Continuity of Functions

Date: 09/15/2004 at 01:12:06
From: Myrtle
Subject: (no subject)

I know that the absolute value of a continuous function is also 
continuous.  Is the opposite true?  That is, if the absolute value of a 
function is continuous, is the function continuous?  If not always true, 
can you give me a counter-example?

Date: 09/15/2004 at 02:03:44
From: Doctor Luis
Subject: Re: continuous absolute value of discontinuous function

Hi Myrtle,

Here's an example:

    http://mathforum.org/dr.math/gifs/myrtle9.14.04.jpg 

The answer should be clear now :-)

Let us know if you have any more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/