设f(x)在(0,+∞)上有意义,x1>0,x2>0,求证：(1)若f(x)/x单调减少,则f(x1+x2)f(x1)+f(x2)；

Question

设f(x)在(0,+∞)上有意义,x1>0,x2>0,求证：
(1)若f(x)/x单调减少,则f(x1+x2) (2)若f(x)/x单调增加,则f(x1+x2)>f(x1)+f(x2) ；

Answer 1

由f(x)的定义域为(0,+∞),x1>0,x2>0,故x1+x2>x1,x1+x2>x2,由f(x)/x单调递减,故f（x1+x2)/(x1+x2) ≤ f(x1)/x1 => x1*f(x1+x2)/(x1+x2) ≤ f(x1)f(x1+x2)/(x1+x2) ≤ f(x2)/x2 => x2*f(x1+x2)/(x1+x2) ≤f(x2) 两式相...