1 . (1)已知
,证明:
;
(2)设
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e27526fad7d109f3f1e157352e5fb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580eda2d6abb825698d18d265a7401b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefcc738d395f255dc3518795ce597cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3b8f0a0cb7d7a8e732c33a62fdfacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f1af8d815f4b284bc0de0664bd440d.png)
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名校
解题方法
2 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,判断并证明函数
的单调性;
(3)设
,
,若存在实数m,n(
),使得函数
在区间[m,n]上的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d04bcc342e046321abc203690916602.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45cf196f21e10ce4031d26fefc22f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
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2022-01-21更新
|
716次组卷
|
8卷引用:四川省四川师范大学附属中学2021-2022学年高一上学期12月月考数学试题
四川省四川师范大学附属中学2021-2022学年高一上学期12月月考数学试题江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题(已下线)【新东方】在线数学35江苏省南通市通州区金沙中学2020-2021学年高一上学期第二次调研考试数学试题上海市控江中学2021-2022学年高一上学期期末数学试题(已下线)第13讲 函数的基本性质(8大考点)(3)(已下线)第13讲 函数的基本性质(8大考点)(2)(已下线)专题14函数的基本性质-【倍速学习法】(沪教版2020必修第一册)
名校
3 . 已知函数
.
(1)判断函数
的奇偶性,并证明;
(2)求证:
在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d102f257b33791eb0fa9571b1bcf13f.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
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4 . 已知函数:
且
.
(1)证明:
对定义域内的所有
都成立;
(2)当
的定义域为
时,求证:
的值域为
;
(3)设函数
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca507b9492083d2c881b824dc98e28ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7297210ecc4a06625860ef4215b42f7.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6870269f258c153030dc97c950698675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69b3ada8af24923589888415f4dabe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2f9766c341bc0bd1362e8e2bd9f552.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3141a4cbf5e3e12ccca84f2d0427430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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2020-10-07更新
|
643次组卷
|
2卷引用:四川省成都七中万达学校2019-2020学年高一10月月考数学试题
12-13高一上·四川巴中·期末
5 . 已知函数![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/7b4458986dc24c878b1bc6e464d0a8bd.png)
(Ⅰ)①判断函数的奇偶性,并加以证明;
②若
(-1,1),计算
;
(Ⅱ)若函数
在
上恒有零点,求实数m的取值范围;
(Ⅲ)若n为正整数,求证:
.
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/7b4458986dc24c878b1bc6e464d0a8bd.png)
(Ⅰ)①判断函数的奇偶性,并加以证明;
②若
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/689dd62d1194434b861d6519db247dad.png)
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/e014711e270c4c63bf082ebe16432dcf.png)
(Ⅱ)若函数
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/67ec7745a25e4fa0bdd28a138348d1bc.png)
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/b0b7086aa0ae4cf9a3855b2528f56bad.png)
(Ⅲ)若n为正整数,求证:
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/d00c7b3cc477474ab2a54448b3fbb95c.png)
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解题方法
6 . 已知函数
.
(1)求
的定义域;
(2)求证:函数
为偶函数;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19242a9ae96a740816c35ed4196aa8bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1187306f996c8d4fbc196426a0f2c7c7.png)
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解题方法
7 . 已知函数
.
(1)求
.
(2)求证:函数
在
上是单调减函数.
(3)求函数
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc8cc2fd258f388fb37ed2c6f4c46da.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4474bd87c00ac3ee99ab366527ded109.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
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8 . 已知函数
.
(1)若
,证明:存在
,使
成立;
(2)若
成立;求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c45e0b413ed96301478521ac23fce0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65b86d84efeac69fddfee74e7f751ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8088f8ec22366394c4be41dea55861c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c984d922ddea48e5fd99876acc38becb.png)
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名校
解题方法
9 . 已知函数
,
的图像关于点
中心对称.
(1)求实数
的值:
(2)探究
的单调性,并证明你的结论;
(3)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd492d001a460384ca5c5ad7211561f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf94d64a8aa1de3d76c6fef961f70844.png)
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2024-01-17更新
|
527次组卷
|
2卷引用:四川省隆昌市第一中学2023-2024学年高一下学期开学考试数学试题
名校
10 . 关于
的方程
(
)的解集为
(
),关于
的方程
(
)的解集为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)对于集合
,
,若
,
,则
.求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f691de51576a125a0bdbd8818d5c1013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52854d0ead4737302f4b4706e1f80553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294dbe05fa6c9f166f7f6ccc1f49f20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d0f310fe9ce9d36f53050e33eada78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c50fb5615e36df436d747356b00d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2333f966f6ec29f0661f93d99b055cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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