Question

设集合A={(X,Y)}|Y≥|X-2|,X≥0}B={(x,y)|y≤-x+b},若A交于B不等于空集,求B取值范围

求解题过程欲详细越好

Answer 1

A={(X,Y)}|Y≥|X-2|,X≥0}
-y≤x-2≤y
2-y≤x≤y+2

B={(x,y)|y≤-x+b},
y≤-x+b
x≤-y+b

要使A交于B不等于空集，则2-y≤x≤y+2,x≤-y+b有解
则2-y≤x≤-y+b有解
所以2-y≤-y+b
b≥2

Answer 2

B>=2
数形结合易得

Answer 3

)}|Y≥|X