Question

设函数f(x)在定义域R上总有f(x)=-f(x+2),且当x大于-1小于等于1时,f(x)=x^2+2 (1)当x大于

Answer 1

因为f(x)= - f(x+2)

即f(x+2) = - f(x)

把左右的x都换成x+2时,

f(x+4) = - f(x+2) = - [ - f(x) ]=f(x)

根据周期函数的定义,f(x)是周期为4的周期函数,

当3