Question

定义在R上的函数f(x),满足f(x)=log2(1-x) x≤0; f(x)=f(x-1)-f(x-2) x>0,求f

Answer 1

x>0

f(x)=f(x-1)-f(x-2)

f(x-1)=f(x-2)-f(x-3)

f(x)=-f(x-3)

f(x-3)=f(x-4)-f(x-5)

f(x-4)=f(x-5)-f(x-6)

f(x-3)=-f(x-6)

f(x)=f(x-6)

f(x+6)=f(x)

f(2012）=f(2+335*6)=f(2)

f(-1)=log2(2)=1

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f(0)=log2(1)=0

f(1)=f(0)-f(-1)=-1

f(2)=f(1)-f(0)=-1

f(2012）=-1