Question 703327
<pre>
|x + 1|  we set x + 1 = 0 and get x = -1, so

|x + 1| means x + 1 if x <u>></u> -1 and -x-1 if x < -1  

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|2x - 1|  we set 2x - 1 = 0 and get x = {{{1/2}}}, so

|2x - 1| means 2x - 1 if x <u>></u> {{{1/2}}} and -2x +1 if x < {{{1/2}}} 

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|x² + 1| means x² + 1 because x² + 1 is always positive. 

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|1 - 2x²|  We set 1 - 2x² = 0 and get 
                    -2x² = -1
                      x² = {{{1/2}}}
                       x = {{{"" +- sqrt(2)/2}}} , so

|1 - 2x²| means 1-2x² if {{{"" - sqrt(2)/2}}} <u><</u> x <{{{"" + sqrt(2)/2}}}

and -1 + 2x² otherwise.

If this isn't what you mean, you can express what you mean
in the thank you note and I'll email you.

Edwin</pre>