名校
1 . 已知函数
,
,
,
,有
成立,则实数
的取值集合为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d95eb357b93c904c43633378d845eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a525d02c2aeb5be4f3ae1de5811c654d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbc5ea3dfd4723d8b76af04493ce4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce41b9226ea83c88bd18a631aa4c8a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1619068c6812df78c4789dc729ee69c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 已知奇函数
的定义域为
.
(1)判断函数
的单调性,并用定义证明;
(2)若实数
满足
,求
的取值范围;
(3)设函数
,若存在
,存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9f333cee2ccb2b215d93011a162f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591c834eb8bd3d34fdad403152ae85db.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8234aaf7d0089aab17c5e999e35cfd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f9d7da5ef0d6b11a30f706f748b7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2261a56462765bd5b87670ebb8949930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e6006eacca1a448fe6991f3c121f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3bb43da17137e6c50874a8086df278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
3 . 已知函数
,
.
(1)若函数
,
,求
的最值;
(2)设函数
,
在区间
上连续不断,证明:函数
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edecfbf1b4e1052468d209e8f017a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce2bfe6e1fde9265d2a07c42bbdf58.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bfb22bf37b71482bd4649852a7dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc17049fc86f1ef6b73f8a14fc24d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f77f8111c7805e673a644b0a690dcc.png)
您最近一年使用:0次
解题方法
4 . 已知函数
(
,
,
)是偶函数,且
,
.
(1)求
的解析式;
(2)若函数
在区间
(
,
,
)上的值域是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f5f43c0785e030c38a96c60b64900d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f306d2b261f4c39a9fc0858d96e647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e454c054f0d2e49716e374c7ce9ac2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a932690fc2a972342433ad38a957c8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b07189fb8e34ccdc581907f16081a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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|
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3卷引用:河南省青桐鸣2023-2024学年高一上学期12月联考数学试题(北师大版)
名校
5 . 已知函数
(
且
).
(1)若
,且
,求
的定义域;
(2)若
,函数
的定义域为
,存在
,使得
在
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f30729daf2fbe0f8f339608cd64e30.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/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313c921defe84689aefde4773ad2b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119b20f27ee885c82edf447d24cc0cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
6 . 设区间A是函数
定义域的一个子集,若存在
,使得
成立,则称
是
的一个“不动点”,也称
在区间A上存在“不动点”,例如
的“不动点”满足
,即
的“不动点”是
.
(1)若函数
有两个互为相反数的“不动点”,求实数a的值:
(2)若函数
在区间
上不存在 “不动点”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4994b0dae849313166b4dc20049a8650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9852d7433cf82fb187fcb796eb6d98d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f74f76d8f930f3086843afe7911f537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b1eccb247386eb3469132edb2d97d6.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97f3f5b347190dd09ed50b3d28d4de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
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2023-12-20更新
|
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2卷引用:黑龙江省哈尔滨市第九中学校2023-2024学年高一上学期12月月考数学试卷
名校
解题方法
7 . 已知函数
,
,其中
,
.
(1)证明:
;
(2)若
,求实数
的值;
(3)问是否存在实数
,使得函数
的定义域为
时,其值域恰好为
?若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095897564b2bb696f4cb3e8016b3fa01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70d3d06b06ec518a2d171b62304bccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7b459051885f09735db25862878159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d61c2a73aed7ffff74baa4f0460fb00.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e541585024d5799abc7184aaea52f0b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfe560ec40006cb5f89f54d8e7540ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)问是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa208c8bab34df3e76f87552abc985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f67001e8efa767d4b2a693745bdba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
8 . 已知函数
,若
满足
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0073ff15f0abcdc2d2e4c1590a9b2307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a24e6b880f731f7d5f42231d9e1e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-19更新
|
1138次组卷
|
6卷引用:上海市东华大学附属奉贤致远中学2023-2024学年高一上学期12月教学评估数学试题
上海市东华大学附属奉贤致远中学2023-2024学年高一上学期12月教学评估数学试题上海市奉贤区2022-2023学年高一上学期1月期末练习数学试题(已下线)专题03 函数性质的综合问题-【寒假自学课】(人教A版2019)江苏省苏州市南航苏州附中2024届高三上学期零模模拟数学试题江苏省镇江市扬中市第二高级中学2023-2024学年高三下学期期初检测数学试题(已下线)第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
9 . 已知
.
(1)当
时,解不等式
;
(2)若关于x的方程
的解集中恰好有一个元素,求实数a的值;
(3)若对任意
,函数
在区间
上总有意义,且最大值与最小值的差等于2,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f782ac135ebb68ffe809837006c8f6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b783ec4871b338c9612cbc700694e7.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e6185447373cdf38c28ba73415637c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983fa8d30993077d136d644a4de7a394.png)
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名校
10 . 在函数定义域内,若存在正实数
,使得函数在区间
上的值域为
则称此函数为“
档类正方形函数”(其中
),已知函数
.
(1)当
时,求函数
的值域;
(2)当
时,是否存在
,使得函数
为“
档类正方形函数”?若存在,求出实数
的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a6162adc13ebe4c5cd3df7d5176d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e151310fd02cd9c47e8892609ddde1c5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2e48341bf9ce1d6ba26b31616f97b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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