已知偶函数f(x)满足f(x)=f(x+3),且f(1)=-1,则f(2)+f(5)的值为

问题描述:

已知偶函数f(x)满足f(x)=f(x+3),且f(1)=-1,则f(2)+f(5)的值为

f(2)
= f(-1 + 3)
= f(-1)
= f(1)
= -1
f(5)
= f(2 + 3)
= f(2)
= -1
所以f(2) + f(5) = -2

f(2)+f(5)=2f(2)=2f(-2)=2f(1)=-2

已知f(x)=f(x+3),取x=-2
f(-2)=f(1)=-1
偶函数f(x),f(2)=f(-2)=-1
取x=2
f(2)=f(5)=-1
f(2)+f(5)=-2