Question

Matemat ..Explicitati modulul :a) /x-2/;b) /1-x/; c)/3x-6/ d) /10-5x/..va rog urgent

Answer 1

/x-2/>0 daca x-2> 0=>x>2
|x-2|<0 daca x-2<0=> x<2
=> x∈R/{2}
|1-X|>0 DACA 1-x>0=>-x>-1=>x<1
|1-x| <0 daca 1-x<0=>-x<-1=> x>1
=> x∈R/{1}
|3x-6|>0 daca 3x-6>0=>x>2
|3x-6|<0 daca |3x-6|<0=>x<2
=>x∈R/{2}

Answer 2

$a)~|x-2|= \left \{ {{x-2,~daca~x \geq 2} \atop {2-x,~daca~x\ \textless \ 2}} \right. ~. \\ \\ b)~|1-x|= \left \{ {{1-x,~daca~x \leq 1} \atop {x-1,~daca~x\ \textgreater \ 1}} \right. ~. \\ \\ c)~|3x-6|= \left \{ {{3x-6,~daca~x \geq 2} \atop {6-3x,~daca~x\ \textless \ 2}} \right. ~. \\ \\ d)~|10-5x|= \left \{ {{10-5x,~daca~x \leq 2} \atop {5x-10,~daca~x\ \textgreater \ 2}} \right. ~.$

$De~retinut:~|a|=a,~daca~a \geq 0~si~|a|=-a,~daca~a\ \textless \ 0.$