當(dāng)x=y=0時(shí),4f(0)*f(0)=2f(0) f(0)=1/2
當(dāng)y=1時(shí),4f(x)*f(1)=f(x+1)+f(x-1)
已知f(1)=1/4
則f(x)=f(x+1)+f(x-1) f(x+1)=f(x)-f(x-1)
所以f(x)=f(x-1)-f(x-2) (1)
f(x-1)=f(x-2)-f(x-3) (2)
(1)+(2)得 f(x)=f(x-3)是周期為3的周期函數(shù)
故f(2010)=f(2010-3)=f(2007)=f(2004)=.=f(0)=1/2