定义在R上的偶函数f(x)在[0,+∞)上递增,且f(12)=0,则满足xf(x)<0的x的取值范围是()A.(0,+∞)B.(0,12)∪(-∞,-12)C.(0,12)∪(12,2)D.(0,12

题目简介

定义在R上的偶函数f(x)在[0,+∞)上递增,且f(12)=0,则满足xf(x)<0的x的取值范围是()A.(0,+∞)B.(0,12)∪(-∞,-12)C.(0,12)∪(12,2)D.(0,12

题目详情

定义在R上的偶函数f(x)在[0,+∞)上递增,且f(
1
2
)=0
,则满足xf(x)<0的x的取值范围是(  )
A.(0,+∞)B.(0,
1
2
)∪(-∞,-
1
2
C.(0,
1
2
)∪(
1
2
,2)
D.(0,
1
2
题型:单选题难度:中档来源:不详

答案

由偶函数f(x)在区间(0,+∞)上单调递增,且f(class="stub"1
2
)=0可知函数在(-∞,0)上递减,且f(-class="stub"1
2
)=0,
∵xf(x)<0
x<0
f(x)>0
x>0
f(x)<0

x<0
x>class="stub"1
2
或x<-class="stub"1
2
x>0
-class="stub"1
2
<x<class="stub"1
2

∴x<-class="stub"1
2
0<x<class="stub"1
2

故选B

更多内容推荐