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《全日制十年制学校高中课本·数学》第一册p.39页习题二中有这样一道题目: “下列函数哪些是奇函数、偶函数?哪些不是奇函数也不是偶函数? (1) f(x)=5x+3;(2) f(x)=5x;(3) f(x)=x~2+1;(4) f(x)=x~2+2x+1;(5) f(x)=x~(-2)+x~4;(6) f(x)=x~(-3)+x。”易知(2)(6)是奇函数,(3)(5)是偶函数,(1)(4)不是奇函数也不是偶函数。但是对于任何一个初等函数是否仅为以上三种类型呢?根据函数的奇偶性。一个函数可以
In the book “Full-time 10-year school high school textbooks and mathematics”, p. 39, exercise 2, there is such a question: “Which of the following functions are odd and even functions? Which are not odd functions nor even functions? (1) f(x)=5x+3; (2) f(x)=5x; (3) f(x)=x~2+1; (4) f(x)=x~2+2x+1;( 5) f(x)=x~(-2)+x~4;(6) f(x)=x~(-3)+x."Yi Zhi(2)(6) is an odd function,(3) (5) is an even function, and (1) (4) is not an odd function nor an even function. But for any elementary function is only the above three types? According to the parity of the function. A function can