已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x,y∈R)则f(2010)=答案是1/2

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已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x,y∈R)则f(2010)=答案是1/2已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+

已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x,y∈R)则f(2010)=答案是1/2
已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x,y∈R)
则f(2010)=
答案是1/2

已知函数f(x)满足f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y)(x,y∈R)则f(2010)=答案是1/2
令:x=1,y=0
得:4f(1)f(0)=2f(1)
f(0)=2*1/4=1/2
令:y=1
得:f(x)=f(x+1)+f(x-1)
f(x-1)=f(x)+f(x-2)
以上两式相加得:f(x+1)+f(x-2)=0
f(x-2)+f(x-5)=0
f(x+1)=f(x-5)
f(x)周期为6
f(2010)=f(6*335)=f(0)=1/2
故:f(2010)=1/2