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函数方程是数学竞赛中的重要内容,在近几年的高校自主招生考试中也有所涉及,一般难度较大,求解的要求较高.函数方程的问题难在已知条件很少,很多问题的已知条件只有一个等式,而且条件比较抽象,无法进行常规的运算.这就要求我们要充分利用已知条件,尽可能地去分析一个表达式的两重含义,也即利用“算两次”得到新的等式或新的条件去解决问题,这种方法在函数方程的求解中应用极为普遍.本文就求解函数方程
The function equation is an important part of the mathematics competition. It has also been involved in the independent college entrance examination in recent years, which is generally more difficult and has higher requirements for solving the problem. The difficulty of the function equation is that there are few known conditions and many problems Known conditions have only one equation, and the conditions are more abstract, can not be conventional operations.This requires us to make full use of known conditions, as far as possible to analyze the two meanings of an expression, that is, using Times "to get new equations or new conditions to solve the problem, this method is very common in the solution of the functional equation.This paper solves the functional equation