已知函数f(x)=2sin(2x-π/4),若f(x+a)为奇函数,a∈[0,2π),求a,若为偶函数,求a
问题描述:
已知函数f(x)=2sin(2x-π/4),若f(x+a)为奇函数,a∈[0,2π),求a,若为偶函数,求a
答
函数f(x)=2sin(2x-π/4),若f(x+a)为奇函数,y=sinx为奇函数f(x+a)=2sin(2(x+a)-π/4)=2sin(2x+2a-π/4)2a-π/4=kπ2a-π/4=0 a=π/8或2a-π/4=πa=5π/82a-π/4=2π a=9π/82a-π/4=3π a=13π/8若为...