已知偶函数f(x)满足f(x+1)=f(x-1),且x∈[0,1],f(x)=(x-1)²,则f(7/2)=
问题描述:
已知偶函数f(x)满足f(x+1)=f(x-1),且x∈[0,1],f(x)=(x-1)²,则f(7/2)=
答
f(x+1)=f(x-1)
则f(x+2)=f(x)
所以 T=2
所以f(7/2)=f(7/2-4)
=f(-1/2)
偶函数
=f(1/2)
=(1/2-1)²
=1/4