奇函數(shù)乘偶函數(shù)

奇函數(shù)乘以偶函數(shù)等于奇函數(shù)。此外，偶函數(shù)乘以偶函數(shù)還等于偶函數(shù)，奇函數(shù)乘以奇函數(shù)等于偶函數(shù)。函數(shù)的奇偶性也就是指關(guān)于原點(diǎn)的對(duì)稱(chēng)點(diǎn)的函數(shù)值相等，這是屬于函數(shù)的基本性質(zhì)，也就是它們的圖象有某種對(duì)稱(chēng)性的一元函數(shù)。

函數(shù)的奇偶性也就是對(duì)任意xEl，若f(-x)=f(x)，即在關(guān)于y軸的對(duì)稱(chēng)點(diǎn)的函數(shù)值相等，則f(x)稱(chēng)為偶函數(shù);若f(-x)= - f(x)，即對(duì)稱(chēng)點(diǎn)的函數(shù)值正負(fù)相反，則f(x)稱(chēng)為奇函數(shù)。

在平面直角坐標(biāo)系中，偶函數(shù)的圖象對(duì)稱(chēng)于y軸，奇函數(shù)的圖象對(duì)稱(chēng)于原點(diǎn).可導(dǎo)的奇(偶)函數(shù)的導(dǎo)函數(shù)的奇偶性與原來(lái)函數(shù)相反。定義在對(duì)稱(chēng)區(qū)間(或點(diǎn)集)上的任何函數(shù)f(x)都可以表示成奇函數(shù)φ( x)和偶函數(shù)ψ(x)之和。

常用運(yùn)算方法：

奇函數(shù)±奇函數(shù)=奇函數(shù)

偶函數(shù)±偶函數(shù)=偶函數(shù)

奇函數(shù)×奇函數(shù)=偶函數(shù)

偶函數(shù)×偶函數(shù)=偶函數(shù)

奇函數(shù)×偶函數(shù)=奇函數(shù)