Question

y=f(x)是定义域在（0,正无穷）上有单调性,f=(x/y)=f(x)-f(y) 1.求f(1)?2.求证f(xy)=

Answer 1

(1)f(x/y)=f(x)-f(y)且y=f(x)的定义域在（0,正无穷）

令 x=y =1 f(1) = f(1) - f(1) = 0

(2)f(x/y)=f(x)-f(y) 得出 f(x) = f(x/y) + f(y)

令x=xy带入f(xy)=f(xy/y)+f(y) = f(x)+f(y);

(3)y=f(x)是定义域在（0,正无穷）上有单调性 f(0) = 0；f(2)=1 为单调递增

f(x)-f(1/(x-3)) < = 2 = 1+1= f(2)+f(2) 得出x>0 1/x-3 >0 求得 x> 3

f(x/(1/(x-3)) )