题目内容
现有命题:若
,且
的两个区间
上都是增函数,由
在集合
,若认为该命题为真,请给出证明;若认为该命题为假,请对原命题予以补充条件,使原命题能成立;先写出补充条件,然后证明给出的真命题.
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需补充条件:
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需补充条件:
因为:任取
,且
,
①若
,由
在
是增函数,必有
成立;
②若
,由
在
是增函数,必有
成立;
③若
,由题设知
且
,
又∵
,∴
,
综上所述,
在
上是增函数.
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因为:任取
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①若
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②若
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③若
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又∵
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综上所述,
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