已知函数f(x)满足f(2)=1/2,2f(x)f(y)=f(x+y)+f(x-y),则f(2012)=?
问题描述:
已知函数f(x)满足f(2)=1/2,2f(x)f(y)=f(x+y)+f(x-y),则f(2012)=?
答
令y=2,根据f(2)=1/2,2f(x)f(y)=f(x+y)+f(x-y)有f(x)=f(x+2)+f(x-2)x=2010 f(2010)=f(2012)+f(2008)x=2008 f(2008)=f(2010)+f(2006)两式相加:f(2012)+f(2006)=0x=2004 f(2004)=f(2006)+f(2002)x=2002 f(2002)=f(2004...