若-3≤log1/2x≤-1/2,求f(x)=(log2 x/2）*(log2 x/4)的最大值和最小值如题

若-3≤log1/2x≤-1/2,求f(x)=(log2 x/2）*(log2 x/4)的最大值和最小值如题
若-3≤log1/2x≤-1/2,求f(x)=(log2 x/2）*(log2 x/4)的最大值和最小值
如题

若-3≤log1/2x≤-1/2,求f(x)=(log2 x/2）*(log2 x/4)的最大值和最小值如题
-3≤log1/2(x)≤-1/2
1/2≤log2(x)≤3
f(x)=[log2(x/2)][log2(x/4)]
=[log2(x)-1][log2(x)-2]
=[log2(x)]^2-3log2(x)+2
=[log2(x)-3/2]^2-1/4
log2(x)=3/2时,有
f(x)min=-1/4
log2(x)=3时,有f(x)max=2