定義一種新運(yùn)算:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319400821080.png)
,已知函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319400981004.png)
,若函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940114643.png)
恰有兩個(gè)零點(diǎn),則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940129312.png)
的取值范圍為( ).
試題分析:這類問題,首先要正確理解新運(yùn)算,能通過新運(yùn)算的定義把新運(yùn)算轉(zhuǎn)化為我們已經(jīng)學(xué)過的知識,然后解決問題.本題中
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940192478.png)
實(shí)質(zhì)上就是取
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940207396.png)
中的最小值,因此
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940223447.png)
就是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940238426.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940254492.png)
中的最小值,函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940285549.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940301535.png)
上是減函數(shù),函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940316595.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940301535.png)
上是增函數(shù),且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940348646.png)
,因此當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940363582.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940379707.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940394643.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940410709.png)
,因此
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319404261422.png)
,由函數(shù)的單調(diào)性知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940441368.png)
時(shí)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940223447.png)
取得最大值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940472543.png)
,又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940363582.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940223447.png)
是增函數(shù),且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319405351032.png)
,,又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940394643.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940223447.png)
是減函數(shù),且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319405821096.png)
.函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940114643.png)
恰有兩個(gè)零點(diǎn),說明函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940628565.png)
的圖象與直線
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940644432.png)
有兩個(gè)交點(diǎn),從函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940223447.png)
的性質(zhì)知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031940675486.png)
.選B.
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