若x1=1,x2=2,则f(x1)=4,f(x2)=7,|f(x1)-f(x2)|=3≤1=|x1-x2|不成立.
(2)对任意两个自变量x1,x2∈(1,+∞),g(x)=a(x−
1 |
x |
因为|g(x1)-g(x2)|=|a(x1−
1 |
x1 |
1 |
x2 |
x2−x1 |
x1x2 |
=|a|•|x1−x2|•|1−
1 |
x1x2 |
⇒|a|•|1−
1 |
x1x2 |
1 | ||
|1−
|
又x1>1,x2>1⇒x1x2>1⇒|1−
1 |
x1x2 |
1 | ||
|1−
|
即|a|≤1
故a的取值范围是:[-1,1]
1 |
x |
1 |
x |
1 |
x1 |
1 |
x2 |
x2−x1 |
x1x2 |
1 |
x1x2 |
1 |
x1x2 |
1 | ||
|1−
|
1 |
x1x2 |
1 | ||
|1−
|