名校
解题方法
1 . 已知函数
是定义在
上的奇函数,且
.
(1)求函数
的解析式;
(2)判断并用定义法证明
在
上的单调性;
(3)解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb474dac35d7d9b9b823f5fdb8db266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f2ef95d5254995f52a67c732b51243.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断并用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(3)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2a0f02510cbf59115751ba5a6e60d7.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,对任意的
有
,且
的最大值为
.
(1)求
的值;
(2)若
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d03b273b7ef759a13b182c73a177a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5426cfddad035627e90cf14078220e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b809c7fd4d5d853c923bfa2e5a855d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557bf8537dbdc00c6a1d1a0bae6d5033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
3 . 已知函数
在定义域
上为偶函数,并且函数
.
(1)判断
的奇偶性,并证明你的结论;
(2)设
,若对任意的
,总存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152043781d916de477d7611cb683a67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c379c978805211415624917ef4c2c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ca37214184b7f655c7810851d3b72.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8336841b5bc3cb4913835080b9d85933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9d255ca420fa2486b11fcb7763b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e6006eacca1a448fe6991f3c121f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bc85e19745af6992cbb72c3fd79ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
名校
解题方法
4 . 设
是定义在
上的奇函数,且对任意实数
,恒有
,当
时
.
(1)求证:
是周期函数;
(2)当
时,求
的解析式;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d78dec1c1e00ec02d7bdaf76ef8901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3262781afb71e9dffc0b7fa1fe280cb2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad814089e37543b2f547af9ae75b6dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f4d3928111ed08cff652ace4e94ae8.png)
您最近一年使用:0次
名校
5 . 已知函数
对任意实数
恒有
,且当
时,
,又
.
(1)判断
的奇偶性;
(2)判断
在
上的单调性,并证明你的结论;
(3)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104fc7daa1aaefd69764e2616109a4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfdecc7f8089cb23c20d0a93ee1b601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64337ab40bd006e29941ca6c4e2e26.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd0380c2d721289573e045c18327ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d871e0c093d338bf3cb3265464aa5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-01-13更新
|
599次组卷
|
2卷引用:福建省福州市鼓山中学2023-2024学年高一上学期12月适应性训练数学试题
名校
6 . 已知函数
对任意的x,
,都有
,且当
时,
,
.
(1)判断函数
的奇偶性,并证明当
时,
;
(2)判断函数
在区间
上的单调性,并用定义法证明;
(3)设实数
,求关于x的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2357ed8dbe6d3911738b8f747d670d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51661fd357fdccf16a18ceaa0601afbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8488679e2fa13e44ffa5b4d802848d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8b1913d38424632464b0a46ddaf0f6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2484f4dc493a45dae01bb8d385ee14e5.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
(3)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68783e70fe281480b7367af89fd51bc.png)
您最近一年使用:0次
名校
7 . 已知定义在
上的函数
满足
,当
时,
,且
.
(1)求
;
(2)判断
的奇偶性,并说明理由;
(3)判断
在
上的单调性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1354afc99cadcf6070d6d15861aff0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad437e8992879263760f235e0ba71c3.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
您最近一年使用:0次
2023-12-30更新
|
431次组卷
|
3卷引用:山东省跨地市多校2023-2024学年高一上学期模拟选课走班调考(12月)数学试题
山东省跨地市多校2023-2024学年高一上学期模拟选课走班调考(12月)数学试题 山东省跨地市多校联考2023-2024学年高一上学期12月月考数学试题(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)
名校
解题方法
8 . 设函数
对任意
,
都有
,且当
时,
.
(1)求
的值;
(2)求证:
为奇函数;
(3)解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57d99676a4c79c2f8d9e84e67386e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)求证:
![](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/34afe69b102d7d9b75b358b5683e687c.png)
您最近一年使用:0次
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49e790b1d37f231c10c6c93facc372c.png)
(1)判断函数的奇偶性,并加以证明;
(2)证明:函数
在
上是减函数;
(3)解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49e790b1d37f231c10c6c93facc372c.png)
(1)判断函数的奇偶性,并加以证明;
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7db30aad0444171fa759bc565ad446.png)
您最近一年使用:0次
2023-12-03更新
|
125次组卷
|
2卷引用:福建省三明市四地四校2023-2024学年高一上学期期中联考数学试题
解题方法
10 . 已知函数
.
(1)用定义法证明函数
在
上单调递增;
(2)若函数
在定义域上为奇函数,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eeb8a56cc02e57775b35f9378e538b1.png)
(1)用定义法证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
您最近一年使用:0次
2023-11-25更新
|
158次组卷
|
4卷引用:四川省泸州市纳溪中学校等四校2023-2024学年高一上学期第一次联考数学试题
四川省泸州市纳溪中学校等四校2023-2024学年高一上学期第一次联考数学试题(已下线)【第三课】3.3幂函数四川省泸州市合江县马街中学校2023-2024学年高一上学期期中数学试题(已下线)3.3幂函数 【第三课】“上好三节课,做好三套题“高中数学素养晋级之路