Question

已知f(x)是定义在{x|x>0}上的单调增函数,且对定义域任意x,y都有f(x乘以y)=f(x)+f(y),且f(2)

Answer 1

(1)

f(x) = f(x * 1) = f(x) + f(1)

所以 f(1) = 0

(2)

由于 f(2x) = f(x) + f(2) = f(x) + 1

所以 f(4) = 2

而已知 f(x) + f(x-3) = f(x^2 - 3x)