Question

设函数f(x)定义在(0,+无穷）上,对任意a,b ∈(0,+无穷）有f(ab)=f(a)+f(b)

Answer 1

f(1)=f(1*1)=f(1)+f(1), 0=f(1)

x>0时,

0=f(1)=f[x*(1/x)]=f(x)+f(1/x), f(1/x) = -f(x).

x>y>1时, x/y>1.

0>f(x/y)=f(x)+f(1/y) = f(x) - f(y), f(x)