x＞1
y = log 1/2 {x+1/(x-1)-1)}
= log 1/2 {(x-1) +1/(x-1)}
∵x-1＞0
∴(x-1) +1/(x-1) = {根號(hào)(x-1) - 1/根號(hào)(x-1) }^2 + 2 ≥ 2
∵底數(shù)1/2 ＜1
∴當(dāng)真數(shù)(x-1) +1/(x-1)取最小值時(shí),y取最大值
∴ymax = log 1/2 2 = -1