1.①易知函數(shù)定義域關(guān)于原點對稱
②f(-x)=[(-x)^3+(-x)]cos(-x)=-(x^3+x)cosx=-f(x)
所以f(x)為奇函數(shù).
2.①易知函數(shù)定義域關(guān)于原點對稱
②f(-x)=cos(-x)-sin(-x)=cosx+sinx
所以f(x)為既非奇函數(shù)又非偶函數(shù).
3.同題2,易判斷知f(x)為既非奇函數(shù)又非偶函數(shù).
4.①易知函數(shù)定義域關(guān)于原點對稱
②f(-x)=sin(-x+π/4)+cos(-x+π/4)
=cos[π/2-(-x+π/4)]+sin[π/2-(-x+π/4)]
=cos(x+π/4)+sin(x+π/4)=f(x)
所以f(x)為偶函數(shù).
5.f(x)=sinx(|sinx-3|-3)=sin^2x（sinx-3小于0,去絕對值變號）
f(-x)=sin(-x)[|sin(-x)-3|-3]
=sin(-x)[3-sin(-x)-3]
=sin^2(-x)=sin^2x=f(x)
所以f(x)為偶函數(shù).
【附】判斷一個函數(shù)的奇偶性,首先判斷函數(shù)的定義域是否關(guān)于原點對稱,若不對稱,則非奇非偶；若對稱,則再判斷f(-x)與f(x)的關(guān)系,f(-x)=f(x)為偶,f(-x)=-f(x)為奇,否則為非奇非偶.