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“含参数不等式当变量在一定范围内变化时恒成立,求参数的范围”是当今高考的热点和难点.有一种类型的不等式,教师与学生的求解经历了一个复杂的历程.案例已知函数f(x)=|x-a|+1/x(x>0),(Ⅰ)当a=1时,求f(x)的最小值;(Ⅱ)欲使f(x)≥1/2恒成立,求a的取值范围.这是一个市级模拟考试的试题,对于第(Ⅱ)题,同学几乎都是这样做的.错解欲使f(x)≥1/2恒成立
“Including parameter inequality When the variable changes within a certain range is constant, the scope of the parameter ” is the hot spot and difficult point of the current college entrance examination. There is a type of inequality, the solution of teachers and students has experienced a complicated course. Knowing function f(x)=|xa|+1/x(x>0), (I) When a=1, find the minimum value of f(x); (II) Want to make f(x)≥1/ 2 Heng established, seeking the value range of a. This is a test question of a city-level mock exam. For the question (II), the students almost always do so. The wrong solution wants to make f(x)≥1/2 constant.