函数是中学数学的重要内容之一。它与数学中其它知识有着密切的联系;本文就函数的性质与方程的解给读者介绍一些方法。一、利用函数的对称性例1 已知函数 y=f(x)满足 f(2+x)=f(2-x).试证:方程 f(x)=0的根成对出现;并且若这个方程有四个根,试求这四个根之和。分析:由于 f(2+x)=f(2-x),这说明函数 y=f(x)的对称轴为 x=2,即 f(x)=f(4-x)∴当 x_0是方程 f(x)=0的一个根,同时4-x_0亦一定是 f(x)=0的根,故方程 f(x)=0 The function is one of the important contents of middle school mathematics. It is closely related to other knowledge in mathematics; this paper introduces some methods to the reader on the nature of the function and the solution of the equation. First, the use of the symmetry of the function Example 1 Known function y = f (x) meets f (2 + x) = f (2-x). Testimony: The root of the equation f (x) = 0 pairs appeared; If this equation has four roots, try to sum the four roots. Analysis: Since f(2+x)=f(2-x), this indicates that the symmetry axis of the function y=f(x) is x=2, that is, f(x)=f(4-x) when x_0 is A root of the equation f(x)=0, and 4-x_0 must also be the root of f(x)=0, so the equation f(x)=0