Question

定义在实数集上的函数f（x）满足f(xy)=f(x)+f(y）,且f(x)是区间（0,正无穷大）上的增函数.

Answer 1

令x = y = 1,带入得 f(1)=f(1)+f(1）解得f(1) = 0

令x = y = 0,带入得 f(0)=f(0)+f(0）解得f(0) = 0,

令x = y = -1,带入得 f(1)=f(-1)+f(-1）解得f(-1) = 0,

令x =-1,带入得 f(-y)=f(-1)+f(y）解得f(-y) = f(y).

所以为偶函数.

f(2)的值,知道了 你告诉我 麻烦了!