Question

Scrie fara modul:
a) |x supra -1| , x<0
b) |x supra -1| , x>0
c) |3 supra x| , x<0
d) |3 supra x| , x>0
e) |x-5| , x<0
f) |-x+1| , x<0
g) x supra |x| , x<0
h) -|x| supra x , x>0

Answer 1

$a)~| \frac{x}{-1} |=|-x|=-x~(pentru~ca~x\ \textless \ 0). \\ \\ b)~ | \frac{x}{-1} |=|-x|=x~(pentru~ca~x\ \textgreater \ 0). \\ \\ c)~ | \frac{3}{x}|= -\frac{3}{x}. \\ \\ d)~ | \frac{3}{x} |= \frac{3}{x}. \\ \\ e)~|x-5|=5-x. \\ \\ f)~|-x+1|=-x+1 . \\ \\ g)~ \frac{x}{|x|} = \frac{x}{-x}=-1. \\ \\ h)~- \frac{|x|}{x} =- \frac{x}{x} =-1.$


$De~retinut: \\ \\ |x|= \left \{ {{x,~daca~x \geq 0} \atop {-x,~daca~x\ \textless \ 0}} \right. .$