名校
解题方法
1 . 已知函数
的表达式为
,且
(
).
(1)求实数
的值;
(2)判断函数
的奇偶性并证明;
(3)判断函数
的单调性,并解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed076f12a4e431bc71f43556c0c747d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d1fe42ce285c0c2a0d1880a8dca6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24736c6e9487e5af65d29dd85fa9949a.png)
您最近一年使用:0次
2023-12-15更新
|
269次组卷
|
5卷引用:上海市南洋模范中学2022-2023学年高一上学期11月月考数学试题
上海市南洋模范中学2022-2023学年高一上学期11月月考数学试题(已下线)5.2函数的基本性质(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高一数学精品教学课件(沪教版2020必修第一册)广东省深圳科学高中2022-2023学年高一上学期期中数学试题上海市卢湾高级中学2023-2024学年高一上学期期中数学试题(已下线)5.2.1 函数的奇偶性-数学同步精品课堂(沪教版2020必修第一册)
解题方法
2 . 函数
的定义域为
,若存在正实数
,对任意的
,总有
,则称函数
具有性质
.
(1)分别判断函数
与
是否具有性质
,并说明理由;
(2)已知
为二次函数,若存在正实数
,使得函数
具有性质
.求证:
是偶函数;
(3)已知
为给定的正实数,若函数
具有性质
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2688c3e4089a131193925f8366b108c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd0d2acb9d499719f4ff04334e94cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253893d2bf2b944a6de271463c3e7929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f894492a8126f5f133dec4cd68833.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f1237b460eca4e05b88832844b22ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5606f53ddd9b02fb3c683f3b48fd861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
3 . 已知函数
.
(1)证明:函数
为偶函数;
(2)证明:函数
在区间
上是严格减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3218299047246838faff556990426a.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
您最近一年使用:0次
名校
4 . 已知幂函数
.
(1)求函数
的解析式;
(2)求函数
的定义域、值域;
(3)判断
的奇偶性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1946c6af96c61bb50bd04e654949d50.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
解题方法
5 . 已知
,函数
是偶函数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc6f9ee317f7e505a4865d3c68354d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da911b94ce55a8c3284d9d3a85cb5522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)若关于x的方程
有两个不等根
,
,求
的值;
(2)若
,
,判断函数
的奇偶性,并说明理由;
(3)是否存在实数
,使得对任意
,关于x的方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8e33b7a38d4965a089d8f9f61aa6ec.png)
在区间
上总有3个不等根
,
,
,若存在,求出实数a与
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c68b5e5d935be4762fa35be0f29a9e9.png)
(1)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27925007a780603e6c59a5cf63d08fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5452c267983506a7cb3373e19fd5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb20586cda25e2255bf1aba5c6cf2c32.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e741baefc96890af5bf245939d66e895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fff7c8c260edb3ce51f15f8d617633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265327864c09da34beafeca32e5715bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8e33b7a38d4965a089d8f9f61aa6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9efa67d5033a65e3d83660db8bb7e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2253c1a391344579ceeac505910c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8477ed6c4d8c19638a0c21edb8a3d4d.png)
您最近一年使用:0次
7 . 设
.
(1)判断函数
的奇偶性,并说明理由;
(2)判断函数
在其定义域上的单调性,并说明理山;
(3)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c71f2109a6715a12a16fb0e4aee29b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bc341bcf08ab1b541d8b5c3b78f485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
.
(1)指出函数
的定义域,并求
,
,
,
的值;
(2)观察(1)中的函数值,请你猜想函数
的一个性质,并证明你的猜想;
(3)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062c65958c76053249cd554f447ede2d.png)
(1)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981b2f8d56d6629da4eb1fc8a701fb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe653ed86488f8dcdf2612ac544fe2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fef5f357f94e1e162cc47a99f9ab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ed052ca7a74b575d8a87f078a8eb7f.png)
(2)观察(1)中的函数值,请你猜想函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c467f4e96ed47b377ed8362e65ebc89c.png)
您最近一年使用:0次
2023-01-07更新
|
273次组卷
|
7卷引用:上海市嘉定区封浜高级中学2023届高三上学期期中数学试题
2022高一·上海·专题练习
名校
解题方法
9 . 设函数
(
,
且
).
(1)若
,判断
的奇偶性和单调性;
(2)若
,求使不等式
恒成立时实数
的取值范围;
(3)若
,
且
在
上的最小值为-2,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f1a326456ba10c718efdcf7d525e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.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/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f3df8bf24d2c68add3f3de3efc4147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0fd153871dfb101f21ea7fcb00792a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fbec93189276445b83c6df4e9f4866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1b6a97182bf7e313389bd039241974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-01-04更新
|
425次组卷
|
7卷引用:4.2 指数函数的图像与性质(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高一数学精品教学课件(沪教版2020必修第一册)
(已下线)4.2 指数函数的图像与性质(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高一数学精品教学课件(沪教版2020必修第一册)(已下线)高一上学期期中【压轴60题考点专练】(必修一前三章)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)上海市崇明区横沙中学2024届高三上学期10月月考数学试题(已下线)第五章 函数的概念、性质及应用(压轴必刷30题9种题型专项训练)-【满分全攻略】(沪教版2020必修第一册)上海市进才中学2023-2024学年高一上学期期末考试数学试卷(已下线)期末真题必刷常考60题(22个考点专练)-【满分全攻略】(沪教版2020必修第一册)(已下线)期末真题必刷压轴60题(10个考点专练)-【满分全攻略】(沪教版2020必修第一册)
解题方法
10 . 已知函数
,
.
(1)讨论函数
的奇偶性,并说明理由;
(2)求实数
的取值范围,使
在区间
上是单调函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037eca3cfa3335c225ce7041ee0aa24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944c02f1425e9c700c928b5a542bd04b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71dbce0ccda0f5df7d0555fa23bf770.png)
您最近一年使用:0次