函數f(x)的定義域為R,且滿足:f(x)是偶函數,f(x-1)是奇函數,若f(0.5)=9,則f(8.5)等於() A. -9B. 9C. -3D. 0

函數f(x)的定義域為R,且滿足:f(x)是偶函數,f(x-1)是奇函數,若f(0.5)=9,則f(8.5)等於() A. -9B. 9C. -3D. 0

∵f(x-1)是奇函數,故有f(-x-1)=-f(x-1),即f(-x)=-f(x-2).又∵f(x)是偶函數,得f(x)=-f(x-2),f(x-4)=f(x)對任意x∈R恒成立,可得f(x)的最小正週期為4,∴f(0.5)=f(8.5)=9.故選:B.