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已知f(x)为奇函数,f(x+2)=f(x),当x属于[0,1]时f(x)=2^x-1则f(log2 1/24)=?
人气:205 ℃ 时间:2020-03-12 03:43:49
解答
∵f(x)是奇函数∴f[log(2)(1/24)]=f[-log(2)(24)]=-f[log(2)(24)]=-f[log(2)(16)+log(2)(3/2)]=-f[4+log(2)(3/2)].f(x+4)=f(x+2)=f(x)=-f[log(2)(3/2)]∵0=log(2)(1)<log(2)(3/2)<log(2)(2)=1∴f[log(2)(1/24)]=-2...-f[log(2)(24)] =-f[log(2)(16)+log(2)(3/2)]这步怎么转换 为什么后面是3/2就是log(2)(24)=log(2)(16×3/2)=log(2)(16)+log(2)(3/2)你看我后面的变换就知道为什么我要这样做-2^log(2)(2/3)怎么算先不看负号,是2^log(2)(3/2)吧?设x=log(2)(3/2)∴2^x=3/2。。。这是定义∴2^log(2)(3/2)=2^x=3/2
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