现行教材中,关于奇函数和偶函数是这样定义的: 一般地,如果对于函数f(x)的定义域内任意一个x,都有f(-x)=-f(x),则称f(x) 为这一定义域内的奇函数; 一般地,如果对于函数f(x)的定义域内任意一个x,都有f(-x)=f(x),则称f(x)为 这一定义域内的偶函数. 有些学生认为只要形式上有f(-x)=-f(x),f(x)就是奇函数;有f(-x)=f(x),f(x)就 是偶函数,而与函数f(x)的定义域没有任何关系. 事实上,如果不先看函数的定义域,函数的奇偶性是无法判别的. In current textbooks, odd and even functions are defined as follows: Generally, if there is f(-x)=-f(x) for any x in the domain of function f(x), then we call f( x) is an odd function within this domain; in general, if f(-x) = f(x) for any x in the domain of the function f(x), we call f(x) this The even function in the definition domain. Some students think that if f(-x)=-f(x) formally, f(x) is an odd function; f(-x)=f(x),f(x) is Even functions do not have any relation to the domain of the function f(x). In fact, if you do not look at the domain of the function first, the parity of the function cannot be discriminated.