已知函数f(x)=sin(π/3-2x)(x属于R)

1个回答

  • 解(1)由f(x)=sin(π/3-2x)

    =-sin(2x-π/3)

    当2kπ-π/2≤2x-π/3≤2kπ+π/2,k属于Z时,y是减函数,

    即kπ-π/12≤x≤kπ+5π/12,k属于Z时,y是减函数,

    知函数的减区间为[kπ-π/12,kπ+5π/12],k属于Z.

    (2)由把函数f(x)=sin(π/3-2x)的图像向右平移π/12个单位时

    函数f(x)=sin(π/3-2x)

    变为f(x)=sin(π/3-2(x-π/12))=sin(π/3-2x+π/6)

    =sin(π/2-2x)=cos2x是偶函数,其图像关于y轴对称.

    即经过图像向右平移π/12个单位时,fx的图像关于y轴对称