问题标题:
【已知f(x)对一切x,y,满足f(0)≠0,f(x+y)=f(x)·f(y),且当x<0时,f(x)>1(1)求f(0)的值(2)求证:当x>0时,0<f(x)<1(3)求证:f(x)在R上是减函数】
问题描述:
已知f(x)对一切x,y,满足f(0)≠0,f(x+y)=f(x)·f(y),且当x<0时,f(x)>1
(1)求f(0)的值
(2)求证:当x>0时,0<f(x)<1
(3)求证:f(x)在R上是减函数
何国辉回答:
(1)f(0)=f(0+0)=f(0)^2,
f(0)(f(0)-1)=0,
f(0)≠0,f(0)=1;
(2)当x>0时,-xx1,
则x2-x1>0,0
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