已知函数f(x)满足f(3)=1/3,3f(x)f(y)=f(x+y)+f(x-y),求f(1812)

因为f(3)=1/3,3f(x)f(y)=f(x+y)+f(x-y)令y=3,得f(x)=f(x+3)+f(x-3)所以,f(x-3)=f(x)+f(x-6)两式相加,得 f(x+3)+f(x-6)=0即,f(x)=-f(x-9)又,f(x-9)=-f(x-18)所以,f(x)=f(x-18)即,f(x)=f(x+18)所以,f(x)的周期为181812...