已知f(x)是定义域为(0,+无穷)的函数,当x属于(0,1)时,f(x)<0,
求证满足f(xy)=f(x)+f(y)的f(x)是增函数.
參考答案:任意x1,x2∈(0,+∞),x1<x2
x1/x2<1 f(x1/x2)<0
f(x1)-f(x2)
=f(x2*x1/x2)-f(x2)
=f(x2)+f(x1/x2)-f(x2)
=f(x1/x2)
<0
得证
已知f(x)是定义域为(0,+无穷)的函数,当x属于(0,1)时,f(x)<0,
求证满足f(xy)=f(x)+f(y)的f(x)是增函数.
參考答案:任意x1,x2∈(0,+∞),x1<x2
x1/x2<1 f(x1/x2)<0
f(x1)-f(x2)
=f(x2*x1/x2)-f(x2)
=f(x2)+f(x1/x2)-f(x2)
=f(x1/x2)
<0
得证