设偶函数f(x)对任意x∈R,都有f(x+3)=-1f(x),且当x∈[-3,-2]时,f(x)=4x,则f(107.5)=( ) A.10 B.110 C.-10 D.-110
问题描述:
设偶函数f(x)对任意x∈R,都有f(x+3)=-
,且当x∈[-3,-2]时,f(x)=4x,则f(107.5)=( )1 f(x)
A. 10
B.
1 10
C. -10
D. -
1 10
答
因为f(x+3)=-
,故有f(x+6)=-1 f(x)
=-1 f(x+3)
=f(x).函数f(x)是以6为周期的函数.1 −
1 f(x)
f(107.5)=f(6×17+5.5)=f(5.5)=-
=-1 f(2.5)
=-1 f(−2.5)
=1 4×(−2.5)
.1 10
故选B