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5.(人教版第84頁(yè)B組第4題)
已知函數(shù),,且
(1) 求函數(shù)定義域
(2) 判斷函數(shù)的奇偶性,并說(shuō)明理由.
變式1:已知是偶函數(shù),定義域?yàn)?img src="http://thumb.1010pic.com/pic20/38/383819_1/image104.gif">.則 ,
解:函數(shù)是偶函數(shù),所以定義域關(guān)于原點(diǎn)對(duì)稱(chēng).∴,
變式2:函數(shù)的圖象關(guān)于 ( )
A.軸對(duì)稱(chēng) B.軸對(duì)稱(chēng) C.原點(diǎn)對(duì)稱(chēng) D.直線對(duì)稱(chēng)
解:函數(shù)定義域?yàn)?img src="http://thumb.1010pic.com/pic20/38/383819_1/image113.gif">,所以,所以函數(shù)為偶函數(shù),圖像關(guān)于軸對(duì)稱(chēng).
變式3:若函數(shù)是奇函數(shù),則
解:由于是奇函數(shù),∴,
即,
∴,又,∴
設(shè)計(jì)意圖:考察定義域與奇偶性
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