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解题方法
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6577db3b86ec49e6ba8956b7b35af0f1.png)
(1)求函数
的定义域;
(2)若不等式
的解集为
,求
时,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6577db3b86ec49e6ba8956b7b35af0f1.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b99eee8134fce76d13c0703fba58672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . (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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2021-01-04更新
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263次组卷
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4卷引用:重庆市部分学校2020-2021学年高一上学期12月联考数学试题
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3 . 设
,且
.
(1)求
的值及
的定义域;
(2)求
在区间
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb143318f22ac1278a32abca7855ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91288f3376f00e3e4e37376c14f5c81d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69334eb9a65544047760a33ecb73cf95.png)
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4 . 已知集合
,函数
的定义域为
.
(1)求
;
(2)已知集合
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0670a822e569e36d25a4fd15d69e1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac19774a8dbc4056ab91ec60af293e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126fdf5a6e9b2d7c23d57798318da453.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae42d35f2787b85190834e2515a3dc39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29cd450d0feaea9acb27a60430f4a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . (1)对于函数
,若函数定义域为
,求实数
的取值范围;
(2)定义在
上的函数
满足:①
,②当
时,
.求
的值,并证明
在
上是单调增函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b8d3f8237af4ee0ed9e3bc4f8ba076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14571b516a0a9f3e3bc56778e42b3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296217d23cb89ea983f761173956eb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
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解题方法
6 . 求下列函数的定义域.
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57987d293f71ef16046b8113ae0f63be.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933a9cf21c75d2a53e80f5d765b737f1.png)
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7 . 设
.
(1)求函数
的定义域和值域;
(2)判断函数
的奇偶性;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750a67d66269e1cc546d520f96e0c258.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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解题方法
8 . 若函数
.
(1)求
的定义域
;
(2)当
时,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cceb782df1eae1714e2c69d58388102.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599ee186c6c676f03283cb06a6b0ff46.png)
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9 . 已知
.
(1)求
的定义域;
(2)判断
的奇偶性,并证明;
(3)判断
的单调性(不需证明);
(4)求使
成立的
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c8a8af02118cf6f1fcbc437727e386.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(4)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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10 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e5428a2a001baa2ed9c8f33478a0ec.png)
(1)当
时,求函数
的定义域和值域.
(2)求使
成立的x的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03208c3f85e3f0bdc6a3c2a8f4642ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e5428a2a001baa2ed9c8f33478a0ec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753ddd380ed18f61bf76d52e1f3dc6ca.png)
(2)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03535592817f149e4be75f06987fd819.png)
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2020-12-27更新
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502次组卷
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3卷引用:江苏省淮安市六校联盟2020-2021学年高一上学期第三次学情调查数学试题