在研究各种函数时,所谓函数方程具有重要的意义。在研究中学数学教程里的初等函数时,研究了偶性、奇性、周期性等等。这些性貭可释为滿足下列某一函数方程 f(-x)=f(x) (偶性) f(-x)=-f(x) (奇性) f(x+a)=f(x)* (原文为f(a),拟排印有誤——譯注) (周期性)的函数性能。在更深入地研究“函数”这一科目的过程中,就自然地提出确定函数为某一函数方程解的問題。显然,上列方程并不确定一具体函数,因为它們都代表极广泛的函数类。例如,方程 When studying various functions, the so-called function equation has an important significance. When studying the elementary functions in the middle school mathematics tutorial, we studied the evenness, singularity, periodicity, and so on. These properties can be interpreted as satisfying one of the following functional equations f(-x)=f(x) (evenness) f(-x)=-f(x) (oddness) f(x+a)=f ( x)* (Period f(a), quasi-printed incorrectly - annotated) (periodic) function performance. In the more in-depth study of the “function” of the subject, it is naturally proposed to determine the function as a function of the solution of the problem. Obviously, the above equations do not define a specific function because they all represent a very broad class of functions. For example, equation