例析函数奇偶性的应用

• 作 者: 张秀琼
• 机 构: 江西省南康市职业中等专业学校,
• 出 处: 理科考试研究
• 发表日期: 2013年19期
• 关键词: 函数奇偶性 应用 函数的奇偶性 高中数学 热点内容 解题过程 奇函数 考试 高考

函数的奇偶性是函数的重要性质之一,也是日常考试和高考中数学的重点和热点内容之一.它应用广泛,在高中数学的各个分支中都有着极为重要的应用.在解题过程中如果应用得好,常能使难题变易,繁题变简,起到事半功倍的效果例1已知函数f(x),当x,y∈R时,恒有f(x+y)=f(x)+f(y).(1)求证:f(x)是奇函数;(2)如果x∈R+,f(x)<0,并且f(1)=-1/2,试求f(x)在区间[-2,6]上的最值.

The function of the parity is one of the important properties of the function, but also the day-to-day exam and college entrance examination mathematics one of the hot spots and focus.It is widely used in all branches of high school mathematics has an extremely important application.In the process of solving problems If the application is good, it can often make the problem easy, simplify the subject, play a multiplier effect. Example 1 Known function f (x), when x, y∈R, always f (x + y) = f (2) If x∈R +, f (x) <0, and f (1) = - 1/2, suppose f (x) is an odd function; (x) The most significant value in the interval [-2,6].