题目内容
(本小题满分13分) 记函数
的定义域为集合M,函数
的定义域为集合N,集合C={x|m-1<x<m+1,m∈R}求:
(1)集合
,
(2)若
,求实数m的取值范围
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(1)集合
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(1)
;
(2)
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(2)
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本试题主要是考查了集合的运算以及集合间关系的运用。
(1)根据已知函数
的定义域使
得到集合M,函数
的定义域为x>3或x<1,得到集合N,那么可知集合
,
的结论。
(2)因为
利用集合的关系得到参数m的范围。
解:(1)
-------------2分
-------------4分
------------6分
-----------8分
(2)
即
-------------10分
所以
,即
-------------13分
(1)根据已知函数
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(2)因为
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解:(1)
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(2)
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所以
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