1 . (1)求函数
的定义域;
(2)用定义法证明
是(-∞,-3)上的减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecb486437ce9eb440f27ee740a504b4.png)
(2)用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26a883dd831a7b3447d5467c5c4762.png)
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4卷引用:山东省全省大联考2020-2021学年高一上学期模拟选课走班调考数学试题
2 . 计算:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7fc91541293a2461770fde350a95cf.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad1f30402c5acf0eb3655e65f7e9f19.png)
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名校
3 . (1)计算:
;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858b60ae9ee108a179a66ee8fbfe3a89.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbe7ea044718fb7c2c7774f89bc5d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9187a835ecfec7aa01dbe30807caf2b5.png)
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4 . 已知定义域为
的函数
是奇函数.
(1)求
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3079ec350c8ef66b60ff1e1c3afc9e1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ff4a1f5d3ad9d7668fe555e70b774c.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2498444d350a3c60b1f5874b6c4ed67.png)
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5 . (1)化简
;
(2)计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145f4c2e884c28cd605e58971a9e158d.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300341d6478c915127c26413b162edd7.png)
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6 . 已知
,函数
.
(1)当
时,解不等式
;
(2)若函数
只有一个零点,求实数
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f159847aac03a301d6ec4491ea49e3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b53c50a48265f7bc85012534062a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 求下列各式的值:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be7668bffec21c760b756f57392034d.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cae7cb7914235d75399f9a7a51ecb8d.png)
(3)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be7668bffec21c760b756f57392034d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cae7cb7914235d75399f9a7a51ecb8d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f2ed219ec286bbcbc445fb8bb5c31a.png)
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8 . 知函数
,其中
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)当
时,求函数的值域;
(2)当
在区间
上为增函数时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc5e9d4e7ba819e51745f328c3a0881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a47e1d9928003aa4b8c7bcf968ff1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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