名校
1 . 已知函数
,
.
(1)解关于
的不等式
;
(2)若函数
在区间
上的值域为
,求实数
的取值范围;
(3)设函数
,求满足
的
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca163d006b9b46dac2d97c988e6d2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fe697379cc264db4c8921ea0fc2151.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5736cbc2a55718ded2c7cfd5ba44b5.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c319abfa1311ddd6e8ac7ae1aa154079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23e21735e7ddd963a87769e34bac581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c3a131e977fcf182cb3989cbf72fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1340cdb1fd01607ea8af14eaa6d23110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2 . 展示某同学解答的两题:
【题1】已知
,求
的值.
解答:由
,可得
,
所以
,即
,解得
或
,
所以
或
,由于
或
均满足
,故
的值是1或4.
【题2】若函数
在区间(-1,1)内恰有一个零点,求实数
的取值范围.
解答:由
,解得
,
所以,实数
的取值范围是
.
该同学的上述解答都正确吗?若不正确,请说明理由(或举反例说明);
选择其中一个你认为解答错误的题,写出你的正确解答过程.
【题1】已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58b1f9787c9b8596d5b9bc6f0a9c41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
解答:由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58b1f9787c9b8596d5b9bc6f0a9c41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf59f5520b0612aa25731a83b7f48ae.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a805718ede5fb77f776f67af67bd6ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c0bfb1ac4c9091f08ac7172b007053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d9bcbc75ffbf824b9ec266030df358.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b32361241c4906a09dc79db55351bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87a46fbb3f24cc37638c8c25cc6baae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b32361241c4906a09dc79db55351bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87a46fbb3f24cc37638c8c25cc6baae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
【题2】若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1dd5a3a791e266159dcdbd1fbbe657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
解答:由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7703c4bb5f4c0d604cfdcb0993ba809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cdd3ad4b904bee1ebadc9a402a8a453.png)
所以,实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030261c59c4aa6c7ffea06043b4122a4.png)
该同学的上述解答都正确吗?若不正确,请说明理由(或举反例说明);
选择其中一个你认为解答错误的题,写出你的正确解答过程.
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