函数f(x)满足f(x)•f(x+2)=13,若f(0)=2,则f(2010)=( ) A.13 B.2 C.132 D.213
问题描述:
函数f(x)满足f(x)•f(x+2)=13,若f(0)=2,则f(2010)=( )
A. 13
B. 2
C.
13 2
D.
2 13
答
∵f(x+2)=
,∴f(x+4)=f(x).13 f(x)
∵2010=502×4+2,∴f(2010)=f(2)=
=13 f(0)
.13 2
故选C.