Question

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（

Answer 1

(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