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...
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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.
skeeter thank you for answering first...can u kindly explain me why the domain of the second and third is like that ?
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 $\displaystyle x < 0$ , $\displaystyle |x| = -x$
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.
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