Question

若集合A={x丨x²-2x-8<0},B={x丨2-m<x<m}

(1)若m=3，全集U=A∪B，试求A∩（B的补集）；
(2)若A∩B=A，求实数m的取值范围
（3）若A∩B=∅，求实数m的取值范围

Answer 1

1、
A={x|-2<x<4}
B的补集={x|x<=-1或x>=3}
u=A={x|-2<x<4}
suoyi
A∩（B的补集)={x|-2<x<=-1或3<=x<4}
2、
隐含条件：2-m<x<m推出：
2－m＜m得到m＞1
A∩B=A推出A包含于B（A的范围在B的范围或A=B）
画数轴比较
m>4（满足m＞1）
3、
A∩B＝空集么？
画数轴比较
4＜＝2－m或m＜＝－2
又m＞1
则得m无解
m＞

Answer 2

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