题目内容
设已知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956222961.gif)
(1)若
,求f(x)的单调增区间;
(2)若
时,f(x)的最大值为4,求a的值;
(3)在(2)的条件下,求满足f(x)=1且
的x的集合。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956222961.gif)
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956254270.gif)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956269525.gif)
(3)在(2)的条件下,求满足f(x)=1且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956285468.gif)
(1)
(2)1(3)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425726.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425698.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425726.gif)
(1)∵
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956550663.gif)
∴
,
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956566909.gif)
∴f(x)的单调增区间为
,
(2)∵
,∴当
时,
=1,即f(x)的最大值为3+a=4,∴a=1
(3)∵
=1,∴
=
,
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956737956.gif)
∵
,∴x的集合为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425726.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956519748.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956550663.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956566909.gif)
解得:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956566909.gif)
∴f(x)的单调增区间为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425698.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956612254.gif)
(2)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956269525.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956644393.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956659547.gif)
(3)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956675625.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956659547.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956722239.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956737956.gif)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956285468.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133956425726.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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