已知函数f(x)=
(1)求A,(∁RA)∩B; (2)若A∪C=R,求实数a的取值范围. |
(1)由题意
,解得7>x≥3,故A={x∈R|3≤x<7},x-3≥0 7-x>0
B={x∈Z|2<x<10}═{x∈Z|3,4,5,6,7,8,9},
∴(CRA)∩B{7,8,9}
(2)∵A∪C=R,C={x∈R|x<a或x>a+1}
∴
解得3≤a<6a≥3 a+1<7
实数a的取值范围是3≤a<6
已知函数f(x)=
(1)求A,(∁RA)∩B; (2)若A∪C=R,求实数a的取值范围. |
(1)由题意
,解得7>x≥3,故A={x∈R|3≤x<7},x-3≥0 7-x>0
B={x∈Z|2<x<10}═{x∈Z|3,4,5,6,7,8,9},
∴(CRA)∩B{7,8,9}
(2)∵A∪C=R,C={x∈R|x<a或x>a+1}
∴
解得3≤a<6a≥3 a+1<7
实数a的取值范围是3≤a<6