求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域

问题描述:

求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域

y=log2(x/4)×log4(x/2)
=[log2(x)-2]*[0.5log2(x)-0.5]
=0.5[log2(x)]²-1.5log2(x)+1
=0.5[log2(x)-1.5]²-0.125
2≤x≤4
1≤log2(x)≤2
0≤[log2(x)-1.5]²≤0.25
-0.125≤y≤0
函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域是[-0.125,0]