設(shè)
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,
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,函數(shù)
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,
(1)設(shè)不等式
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的解集為C,當(dāng)
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時(shí),求實(shí)數(shù)
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取值范圍;
(2)若對(duì)任意
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,都有
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成立,試求
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時(shí),
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的值域;
(3)設(shè)
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,求
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的最小值.
(1)
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(2)
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值域?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222411478505.png" style="vertical-align:middle;" />.
(3)
本試題主要是考查了函數(shù)的性質(zhì),單調(diào)性和定義域和最值,值域問(wèn)題。以及集合的運(yùn)算等知識(shí)點(diǎn)的綜合運(yùn)用。
(1)根據(jù)不等式的解集與已知兩個(gè)集合的并集的關(guān)系,分析得到參數(shù)m的取值范圍。
(2)由題可知函數(shù)有一條對(duì)稱軸方程x=1,然后根據(jù)這一點(diǎn)得到m的值,然后分析給定區(qū)間的二次函數(shù)的最值。
(3)因?yàn)榻o定的函數(shù)中帶有絕對(duì)值符號(hào),因此要根據(jù)絕對(duì)值的定義寫為分段函數(shù),然后分別對(duì)于含有參數(shù)的二次函數(shù)的最值作出分析和求解即可。
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