定义在R上的偶函数满足:对任意x1,x2∈[0,+∞),且x1≠x2都有
|
∵(x2-x1)(f(x2)-f(x1))>0,
∴
>则f(x)在x1,x2∈[0,+∞)(x1≠x2)上单调递增,f(x2)-f(x1) x2-x1
又f(x)是偶函数,故f(x)在x1,x2∈(-∞,0](x1≠x2)单调递减.
且满足n∈N*时,f(-2)=f(2),3>2>1>0,
得f(1)<f(-2)<f(3),
故选B.
定义在R上的偶函数满足:对任意x1,x2∈[0,+∞),且x1≠x2都有
|
∵(x2-x1)(f(x2)-f(x1))>0,
∴
>则f(x)在x1,x2∈[0,+∞)(x1≠x2)上单调递增,f(x2)-f(x1) x2-x1
又f(x)是偶函数,故f(x)在x1,x2∈(-∞,0](x1≠x2)单调递减.
且满足n∈N*时,f(-2)=f(2),3>2>1>0,
得f(1)<f(-2)<f(3),
故选B.