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(2012).

问题描述:

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(2012).

x>0f(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--------------------f(0)=log2(1)...