填空题设f(x)=Asin(ωx+?)(A>0,ω>0,x∈R),则f(0)=0是f(x)为奇函数的________条件.
网友回答
充要解析分析:f(0)=0?f(0)=Asin(ω×0+?)=Asin?=0??=kπ,k∈Z?f(x)=Asin(ωx+?)(A>0,ω>0,x∈R)是奇函数.f(x)为奇函数??=kπ,k∈Z?f(0)=Asin(ω×0+kπ)=Asinkπ=0.所以f(0)=0是f(x)为奇函数的充要条件.解答:若f(0)=0,则f(0)=Asin(ω×0+?)=Asin?=0,∴?=kπ,k∈Z,∴f(x)=Asin(ωx+?)(A>0,ω>0,x∈R)是奇函数.若f(x)为奇函数,则?=kπ,k∈Z,∴f(0)=Asin(ω×0+kπ)=Asinkπ=0.所以f(0)=0是f(x)为奇函数的充要条件.故