题目内容
已知
设函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222519978987.png)
(Ⅰ)当
,求函数
的的值域;
(Ⅱ)当
时,若
="8," 求函数
的值;![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520118169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225199471238.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222519978987.png)
(Ⅰ)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222519993705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520009447.png)
|
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222519993705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520009447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520118169.png)
(Ⅰ)函数
的值域为
. (Ⅱ)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520305605.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520243448.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520259570.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520305605.png)
(I)先根据数量积的定义及向量的模的坐标表示以及降幂公式及两角和与差的恒等变换公式求出
,再根据x的范围求值域.
(II)
,再根据
,确定出
,求出
然后把
转化为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
问题到此基本得以解决.
(Ⅰ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225206642391.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225206951921.png)
,
由![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520118169.png)
得
,所以
,则函数
的值域为
.
(Ⅱ)
,
; 所以
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225210851630.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225203371553.png)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225204771259.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520493683.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520508871.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520571969.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225206491188.png)
(Ⅰ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225206642391.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225206951921.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520727913.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520118169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222519993705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520836907.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520851974.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520243448.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520259570.png)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225209921635.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225210231188.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520571969.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823222520087707.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232225210851630.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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