Question

Функция задана формулой у(х)=|2-х|-2
1) найти у (-3), у(-1), у(1), у(3)
2) _найти значение х, если у (х)=-2, у(х)=0 , у(х)=2, у(х)=4.

Answer 1

$y(x)=|2-x|-2, \\ 1)\\ y(-3)=|2+3|-2=3, \\ y(-1)=|2+1|-2=1, \\ y(1)=|2-1|-2=-1, \\ y(x)=|2-3|-2=-1;\\ 2)\\ y(x)=-2, |2-x|-2=-2, \\ |2-x|=0, \\ 2-x=0, \\ x=2; \\ y(x)=0, |2-x|-2=0, \\ |2-x|=2, \\ \left [ {{2-x=-2,} \atop {2-x=2;}} \right. \left [ {{x=4,} \atop {x=0;}} \right. \\ y(x)=2, |2-x|-2=2, \\ |2-x|=4, \\ \left [ {{2-x=-4,} \atop {2-x=4;}} \right. \left [ {{x=6,} \atop {x=-2;}} \right. \\ y(x)=4, |2-x|-2=4, \\ |2-x|=6, \\ \left [ {{2-x=-6,} \atop {2-x=6;}} \right. \left [ {{x=8} \atop {x=-4.}} \right$