f(x)满足f(1)=1/4 4f(x)f(y)=f(x+y)+f(x-y) (x ,y属于R)则 f(2010)=?
问题描述：
f(x)满足f(1)=1/4 4f(x)f(y)=f(x+y)+f(x-y) (x ,y属于R)则 f(2010)=?
答
取y=1,则 4f(x)f(1)=f(x+1)+f(x-1)即 f(x)=f(x+1)+f(x-1)所以 f(x+1)=f(x+2)+f(x) (在上式中,以x+1代替x)两式相加,得 f(x+2)+f(x-1)=0所以 f(x+2)=-f(x-1)因此,f(x+6)=f[(x+4)+2]=-f[(x+4)-1]=-f(x+3)=-f[(x+1)+2]=f...