Question

已知函数f(x)的定义域为(0,正无穷),且f(4)=1,对于任意x1,x2属于(0,正无穷),有f(x1

已知函数f(x)的定义域为(0,正无穷),且f(4)=1,对于任意x1,x2属于(0,正无穷),有f(x1*x2)-f(x1)+f(x2),当x1>x2时有f(x1)>f(x2).求f(1)的值

Answer 1

f(1) = f(1×1) = 2f(1), 故 f(1) = 0.

Answer 2

∵f(4)=f(2X2)=f(2)+f(2)=1,∴f(2)=1/2. 又∵f(2)=f(1X2)=f(1)+f(2)=1/2,∴f(1)=0