函数f(x)的定义域为R,且满足:f(x)是偶函数,f(x-1)是奇函数,若f(0.5)=9,则f(8.5)等于( )
A. -9
B. 9
C. -3
D. 0
人气:472 ℃ 时间:2019-08-21 18:56:36
解答
∵f(x-1)是奇函数,故有f(-x-1)=-f(x-1),即f(-x)=-f(x-2).
又∵f(x)是偶函数,得f(x)=-f(x-2),
f(x-4)=f(x)对任意x∈R恒成立,可得f(x)的最小正周期为4,
∴f(0.5)=f(8.5)=9.
故选:B.
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