f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),x,y∈R,求f(2010)的值.答案是1/2,【求过程】
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![f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),x,y∈R,求f(2010)的值.答案是1/2,【求过程】](/uploads/image/z/14291768-56-8.jpg?t=f%281%29%3D1%2F4%2C4f%28x%29f%28y%29%3Df%28x%2By%29%2Bf%28x-y%29%2Cx%2Cy%E2%88%88R%2C%E6%B1%82f%282010%29%E7%9A%84%E5%80%BC.%E7%AD%94%E6%A1%88%E6%98%AF1%2F2%2C%E3%80%90%E6%B1%82%E8%BF%87%E7%A8%8B%E3%80%91)
f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),x,y∈R,求f(2010)的值.答案是1/2,【求过程】
f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),x,y∈R,求f(2010)的值.答案是1/2,【求过程】
f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),x,y∈R,求f(2010)的值.答案是1/2,【求过程】
先令x=1 y=0得4f(1)f(0)=f(1)+f(1)得f(0)=1/2
令x=1 y=1得4f(1)f(1)=f(2)+f(1)得f(2)=0
.
令x=4 y=1得 f(5)= =1/2
.周期为5
2010/5刚好除尽
答案是1/2
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