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2014年“北约”自主招生试题第3题为:题目设函数f(x)满足:f(1)=1,f(4)=a7,且对任意的a,b∈R,有f(z+2b/3)=f(a)+2f(b)/3,则f(2014)=()3(A)4027.(B)4028.(C)4029.(D)4030.该题以函数方程为载体综合考察了数列及其递推关系和数学归纳法等知识点,看似简单,实则不易.笔者私下了解了我校参加考试学生的答题情况,大部分学生能够正确选出结果,但细究起来发现,很多学生对于该函数方程的处理是兜来兜
In 2014, the third question of the “NATO” self-enrollment test question is: Problem Set the function f (x) to satisfy: f (1) = 1, f (4) = a7, and for any a, b∈R, f f (a) + 2f (b) / 3, f (2014) = () 3 (A) 4027. (B) 4028. (C) 4029. Problems with function equation as a vector comprehensive examination of the sequence and its recurrence relations and mathematical induction and other knowledge points, seemingly simple, but in fact not easy.The author privately understand my school to take the exam students answer the question, most students can correctly selected The result, however, is that as many students have worked out the equation of function