Question

设定义在R上的函数f（x）满足f（x）•f（x+2）=3,若f（1）=2,则f（2011）=______．

Answer 1

f(x)f(x+2)= 3

得f(x+2)= 3/f(x)

f(1)=2

f(3)= 3/f(1)= 3/2

f(5)= 3/f(3)=2

f(7)= 3/f(5)= 3/2

.

所以

f(1)=f(5)=f(9)=...=2

f(3)=f(7)=f(11)=...= 3/2

所以

f(2011)=f(3+2008)=f(3+502×4)=f(3)= 3/2