函数f(x)的定义域是(0,正无穷大),当x>1时,f(x)

函数f(x)的定义域是(0,正无穷大),当x>1时,f(x)<0,f(x.y)=f(x)+f(y),证明f(x)是减

f(x.y) = f(x)+f(y)
令y=1+r(r>0),则f(xy)=f(x+rx) = f(x)+f(1+r)而(1+r)x > x,所以当x增加到(1+r)x时,f(x)减少,所以函数时单调减函数