第3个回答 推荐于2017-11-24
f(x+1)是奇函数,则f(-x+1)=-f(x+1)
f(x-1)是奇函数,则f(-x-1)=-f(x-1) ==>>> f[-(x+2)-1]=-f[(x+2)-1]=-f(x+1)
则:f(-x+1)=f[-(x+2)-1]=f(-x-3) ==>>> f(-x+1)=f(-x-3) ===>>> f(x+1)=f(x-3)
则f(x)是以4为周期的函数,即:f(x)=f(x+4)
又:f(-x+1)=-f(x+1) ===>>> f[-(x+4)+1]=-f[(x+4)+1] ==>>> f(-x-3)=-f(x+5)
f(x+5)=f(x-3)
所以:f(-x-3)=-f(x-3),即:f(x+3)是奇函数。本回答被提问者采纳