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解题方法
1 . 若函数
满足
(其中
且
).
(1)求函数
的解析式,并判断其奇偶性和单调性;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cef8b818a4cac7d67f7c8c16d593b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467df644872d1926a01ac3ef8ba38197.png)
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2 . 已知函数
,
,其中
,且
.
(1)若
,求满足不等式
的
的取值的集合;
(2)求关于
的不等式
的解的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202602fa2f0162ce58bc480ec38e7dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1163c2709d5b503c9821ea9ed7ff93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b61adc4745f283e4072ddd762f92ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
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3 . 定义在
上的函数
对任意的
,满足条件:
,且当
时,
.
(1)求
的值;
(2)证明:函数
是
上的单调增函数;
(3)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c282d2ec29ff3e68bb0e6a86be3dadcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b812ad4c0d31fbe75bdb3e80f170e15.png)
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2017-08-20更新
|
1157次组卷
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4卷引用:山东省潍坊寿光市2016-2017学年高二下学期期末考试数学(文)试题
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4 . 已知函数
在
上是奇函数.
(1)求
;
(2)对
,不等式
恒成立,求实数
的取值范围;
(3)令
,若关于
的方程
有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ea98dd92ead003c07da6de559e53e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5efc0c2ce088df75460293be1ba9d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e55eac8ba4c5f0501294eb4dcd8e573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad60159fda4b592e4a668e5bbfafa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2016-12-04更新
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5卷引用:辽宁省本溪市第一中学2017-2018学年高二上学期第一次月考(理)数学试题
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5 . 设f'(x)是函数f(x)的导数,f''(x)是函数f'(x)的导数,若方程f''(x)=0有实数解x0,则称点(x0,f(x0))为函数f(x)的拐点.某同学经过探究发现:任何一个三次函数f(x)=ax3+bx2+cx+d(a≠0)都有拐点,任何一个三次函数都有对称中心,且拐点就是对称中心,设函数g(x)=x3﹣3x2+4x+2,利用上述探究结果计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a9a8518a1b2bd6069366aa18e6d64a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a9a8518a1b2bd6069366aa18e6d64a.png)
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2018-04-04更新
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4卷引用:2017届四川自贡市高三一诊考试数学(理)试卷
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6 . (1)计算:
;
(2)解关于
的方程:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b739d5173535dc705974f8450d3df68.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13349e1663c90f899a4a9f45b68962f.png)
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2018-01-08更新
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2卷引用:河北省衡水市枣强中学2017-2018学年高一上学期期中考试数学试题
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7 . 若关于x的不等式
至少有一个负实数解,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5eeeea194e569a7e8d9b5b026eba16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2020-03-25更新
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599次组卷
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8卷引用:广西南宁市第三中学2017-2018学年高二上学期期中考试数学试题
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8 . 已知函数
(
常数
)
(1)当
时,解关于
的不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af7267fa641fe998666f090bac90f6e.png)
(2)讨论函数
的奇偶性,并说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b15ebe414d00951198268ca531449c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f6376354865d8699989ccee1c885fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42acea836df9ca7c237b52df778c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b40fc41dac3987acaa766db9a15ad5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af7267fa641fe998666f090bac90f6e.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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9 . 已知函数
.
(1)指出函数
的基本性质:定义域,奇偶性,单调性,值域(结论不需证明),并作出函数
的图象;
(2)若关于
的不等式
恒成立,求实数
的取值范围;
(3)若关于
的方程
恰有
个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d51f20de449bb518d8ccddcd2970a8.png)
(1)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893b785b7c2f2b86a041bbc2317105dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a2f6aa1362f427fa41c9de7110f6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2020-01-30更新
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3卷引用:上海市大同中学2017-2018学年高一上学期期中数学试题
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10 . 若关于x的不等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218790ce1f3b2d3f2659649e9f939bf2.png)
(1)解此不等式;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218790ce1f3b2d3f2659649e9f939bf2.png)
(1)解此不等式;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbbf4669faacac34733670a96d3f1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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