# Thread: difference between absolute value and 'normal' one

1. ## 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...

2. 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...
$\displaystyle g(x) = \frac{x}{x} = 1$ , $\displaystyle x \ne 0$

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

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

graph them to confirm.

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

4. 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 $\displaystyle x \ge 0$ , $\displaystyle |x| = x$

if $\displaystyle x < 0$ , $\displaystyle |x| = -x$

5. Be aware, however, that there is not a "second" and "third". The last two equations are for the same function. And, in fact, $\displaystyle frac{x}{x}$ and $\displaystyle \frac{|x|}{x}$ have exactly the same domains- all x except 0.