1979年全国通用高中数学课本引入“函数周期性”内容之后 ,一直引起人们的关注 .笔者注意到有关判定ｆ(ｘ) =ｓｉｎ1ｘ、φ(ｘ) =3ｃｏｓ ｘ -1(ｘ +1 ) (ｘ-2 ) 等为非周期函数时 ,总是采用反证法加以论证 .这不仅有一定的难度 ,而且也需花费时间 .对于上述ｆ(ｘ)、φ(ｘ)以及 In 1979, the general high school mathematics textbooks in the country introduced the “periodic periodicity” content, which has been attracting people’s attention. The author noticed that the determination f (x) = sin1x, φ (x) = 3cos x -1 (x +1) (x -2) When an aperiodic function is used, it is always demonstrated by counter-evidence. This is not only difficult, but it also takes time. For the above f(x), φ(x) and