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问题: 一道数学题

y=(2cosx+1)/(2cosx-1)的值域是(       )
(负无穷,1/3]并[3,正无穷)

解答:

y = (2cosx+1)/(2cosx-1) = 1 + 2/(2cosx-1)
-1 <= cosx <= 1, -3 <= 2cosx-1 <= 1
负无穷 < 2/(2cosx-1) <= -2/3, 2 <= 2/(2cosx-1) < 正无穷
==> y 的值域是: (负无穷,1/3]and[3,正无穷)