Question

求助一道数学题已知函数f(x)对任意的实数满足f(x+3)=-1/f(x) 且当-3≤x

Answer 1

f(x+6)=f(x+3+3)=-1/f(x+3)=-1/-1/f(x)=f(x) f(x)是以6为周期的周期函数

f(1)=1 f(2)=2 f(3)=f(0+3)=-1/f(0)=-1/f(-3+3)=-1/-1/f(-3)=-1

f(4)=f(1+3)=-1/f(1)=-1 f(5)=f(2+3)=-1/f(2)=-1/2 f(6)=f(3+3)=-1/f(3)=1 f(1)+f(2)+f(3)+f(4)+f(5)+f(6)=3/2

2014/6=370.4 f(1)+f(2)+f(3)+f(4)=1

f(1)+f(2)+f(3).f(2014)=370*3/2+1=556