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数学
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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)=( )
A.
1
2
B.
1
3
C.
1
4
D. 1
人气:491 ℃ 时间:2019-08-21 18:53:58
解答
解法一:∵4f(x)f(y)=f(x+y)+f(x-y)取x=1,y=0得f(0)=12根据已知知f(1)=14取x=1,y=1得f(2)=-14取x=2,y=1得f(3)=-12取x=2,y=2得f(4)=-14取x=3,y=2得f(5)=-14取x=3,y=3得f(6)=12 …猜想得...
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