B
分析:由函數(shù)f(x)是定義在R上的偶函數(shù),則函數(shù)的圖象關(guān)于y軸對(duì)稱(chēng),又由f(1-x)=f(-x-3),則函數(shù)的圖象關(guān)于直線(xiàn)x=-1對(duì)稱(chēng),則易得函數(shù)f(x)是周期為2的周期函數(shù),又由當(dāng)0≤x≤2時(shí),
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,則當(dāng)x=1時(shí),
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,則易求
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成立的x的集合.
解答:∵函數(shù)f(x)是定義在R上的偶函數(shù),
∴函數(shù)的圖象關(guān)于y軸對(duì)稱(chēng),
又∵f(1-x)=f(-x-3),
∴函數(shù)的圖象關(guān)于直線(xiàn)x=-1對(duì)稱(chēng),
∴函數(shù)f(x)是周期為2的周期函數(shù),
又∵當(dāng)0≤x≤2時(shí),
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,
∴當(dāng)x=1時(shí),
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,
∴使
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成立的x的集合為{x|x=2n-1,n∈Z}
故選B
點(diǎn)評(píng):利用函數(shù)的周期性解題要注意:對(duì)于任意實(shí)數(shù)x,①若f(x+T)=f(x),則T為函數(shù)的周期;②若f(x+T)=-f(x),則2T為函數(shù)的周期;③若(a,y),(b,y)分別為函數(shù)的兩個(gè)對(duì)稱(chēng)中心則T=2|a-b|④若x=a,x=b都是函數(shù)的對(duì)稱(chēng)軸,則T=2|a-b|.