摘要:11.已知f(x+2)=f(x)(x∈R).并且当x∈[-1,1]时.f(x)=-x2+1.求当x∈[2k-1,2k+1](k∈Z)时.f(x)的解析式. 解:由f(x+2)=f(x).可推知f(x)是以2为周期的周期函数.当x∈[2k-1,2k+1]时.2k-1≤x≤2k+1.-1≤x-2k≤1.∴f(x-2k)=-(x-2k)2+1. 又f(x)=f(x-2)=f(x-4)=-=f(x-2k). ∴f(x)=-(x-2k)2+1.x∈[2k-1,2k+1].k∈Z.
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