# difference between absolute value and 'normal' one

• Mar 24th 2010, 05:20 PM
alessandromangione
difference between absolute value and 'normal' one
g ( x) = absolute value of x /x and g (x) = x /x

i have to find the domain of each of the functions...what is the difference between them...
• Mar 24th 2010, 06:17 PM
skeeter
Quote:

Originally Posted by alessandromangione
g ( x) = absolute value of x /x and g (x) = x /x

i have to find the domain of each of the functions...what is the difference between them...

$g(x) = \frac{x}{x} = 1$ , $x \ne 0$

$g(x) = \frac{|x|}{x} = 1$ , $x > 0$

$g(x) = \frac{|x|}{x} = -1$ , $x < 0$

graph them to confirm.
• Mar 24th 2010, 06:37 PM
alessandromangione
skeeter thank you for answering first...can u kindly explain me why the domain of the second and third is like that ?
• Mar 24th 2010, 06:39 PM
skeeter
Quote:

Originally Posted by alessandromangione
skeeter thank you for answering first...can u kindly explain me why the domain of the second and third is like that ?

because of the definition of absolute value ...

if $x \ge 0$ , $|x| = x$

if $x < 0$ , $|x| = -x$
• Mar 25th 2010, 03:09 AM
HallsofIvy
Be aware, however, that there is not a "second" and "third". The last two equations are for the same function. And, in fact, $frac{x}{x}$ and $\frac{|x|}{x}$ have exactly the same domains- all x except 0.