已知函数f(X)=log2(X+1),将y=f(X )的图像向左平移一个单位,再将图像上所有点的纵坐标伸长到原来的2倍(

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  • (1)g(x)=2log2(x+2) 定义域x>-2

    (2) F(x)=log2(x+1)-2log2(x+2)=log2(x+1)-log2(x+2)^2

    =log2(x+1)/(x+2)^2=log2(x+1)/(x^2+4x+4)

    =log2(x+1)/[(x+1)^2+2(x+1)+1]

    =log2 1/[(x+1)+1/(x+1)+2]

    ≤log2 1/(2√(x+1)*1/(x+1)+2)

    =log2 1/(4)

    =-2

    所以最大是-2