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全称量词,特称量词,以及全称命题和特称命题在近几年新课标高考卷和模拟卷中频频亮相,成为高考的热点问题.特别是全称量词“任意”和特称量词“存在”与函数情投意合,两种量词插足函数,使得函数问题意深难懂神秘莫测,问题显得更加扑朔迷离,难度大增,同时题目也因此显得富有变化和新意.解决这类问题的关键是揭开量词隐含的神秘面纱还函数问题本来面目,下面结合高考试题对此类问题进行归纳探究.一、问题探究问题2:已知函数2f(x)=2k x+k,x∈[0,1],函数2g(x)=3x-2(k+k+1)x+5,x∈[-1,0],问当k=2时,对任意x1∈[0,1],是否存在x∈[-1,0],使g(x)=f(x)成立.
Full name of quantifier, special measure word, as well as the full name of the proposition and the special title proposition in recent years, the new curriculum exam papers and simulated volume frequently appeared as a hot topic in the college entrance examination. In particular the full quantifier “arbitrary ” and special weighing The word “existence ” and the function of emotion coincide, the two kinds of quantifier interpolation function, making the function difficult to understand mysterious mystery, the problem appears more complicated and confusing, the degree of difficulty greatly increased, at the same time the topic also appears full of change and new ideas.To solve these problems The key is to unveil the hidden mystery of the quantifier also function of the original problem, the following combination of college entrance examination questions to explore such issues I. First, the problem to explore Question 2: Known function 2f (x) = 2k x + k, x ∈ [0,1], the function 2g (x) = 3x-2 (k + k + 1) x + 5 and x∈ [-1,0]. When k = 2, 1], whether x∈ [-1,0] exists, and g (x) = f (x) holds.