设全集是实数集R,A={x|1/2≤x≤3},B={x|-a+1≤x+1≤2a-1},若(CRA)∩B=B,求实数a的取值范围.
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![设全集是实数集R,A={x|1/2≤x≤3},B={x|-a+1≤x+1≤2a-1},若(CRA)∩B=B,求实数a的取值范围.](/uploads/image/z/3797684-44-4.jpg?t=%E8%AE%BE%E5%85%A8%E9%9B%86%E6%98%AF%E5%AE%9E%E6%95%B0%E9%9B%86R%2CA%3D%7Bx%EF%BD%9C1%2F2%E2%89%A4x%E2%89%A43%7D%2CB%3D%7Bx%EF%BD%9C-a%2B1%E2%89%A4x%2B1%E2%89%A42a-1%7D%2C%E8%8B%A5%EF%BC%88CRA%EF%BC%89%E2%88%A9B%3DB%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
设全集是实数集R,A={x|1/2≤x≤3},B={x|-a+1≤x+1≤2a-1},若(CRA)∩B=B,求实数a的取值范围.
设全集是实数集R,A={x|1/2≤x≤3},B={x|-a+1≤x+1≤2a-1},若(CRA)∩B=B,求实数a的取值范围.
设全集是实数集R,A={x|1/2≤x≤3},B={x|-a+1≤x+1≤2a-1},若(CRA)∩B=B,求实数a的取值范围.
CRA=(-∞,1/2)∪(3,+∞),B=[-a,2a-2]
要使(CRA)∩B=B则有B包含于A
B=∅,有2a-1<-a+1有a<2/3
B≠∅,则a≥2/3
要使B包含于A则2a-2<1/2或-a>3
有a<3/2或a<-3
所以B≠∅的条件是a∈[2/3,3/2)
综上,a的取值范围是(-∞,3/2)
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