已知函數(shù)
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(1)用定義證明
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在
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上單調(diào)遞增;
(2)若
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是
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上的奇函數(shù),求
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的值;
(3)若
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的值域為D,且
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,求
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的取值范圍.
(1)設
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且
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則
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即
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在
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上單調(diào)遞增 ;
(2)
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;(3)
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.
試題分析:(1)在定義域內(nèi)任取
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,證明
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,即
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,所以
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在
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上單調(diào)遞增;(2)因為,
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是
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上的奇函數(shù),所以
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,即
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,代入表達式即可得
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;(3)可求得
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的值域
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,由
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可得不等式
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,所以
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.
試題解析:(1)設
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且
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1分
則
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3分
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
即
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5分
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在
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上單調(diào)遞增 6分
(2)
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是
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上的奇函數(shù)

8分
即
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
11分
(用
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得
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必須檢驗,不檢驗扣2分)
(3)由
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

14分
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

的取值范圍是
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16分
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