名校
解题方法
1 . 若非零函数
对任意x,y均有
,且当
时,
.
(1)求
,并证明
;
(2)求证:
为
上的减函数;
(3)当
时,对
时恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6585b5af98d4c7801c1edaf2e6ead0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73ed206046205dc9e41285f74d81dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1dd6e7640a36050cbbbcc6449606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
的图象过点
和
.
(1)求证:
是奇函数,并判断
的单调性(不需要证明);
(2)若
,使得不等式
都成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e55a83e52879f750bf8628f4cf72bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9d132149769927b69d53390602c35b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac776ffa3c5072f5e1918ebb288ec464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 已知函数
的定义域为
,对任意
,
都有
,且
.
(1)求证:
;
(2)判断
奇偶性,并证明;
(3)若
,且
在
上单调递增,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d297e6ee5f46200f2063ed6d92cef50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0641418cf3acf8bf8ce6ed287d68cc87.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512c60d122d0b16427342ae06c93fda5.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a26afd5d8b577a93021e2ad8aee28c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe7bcabcfb85b89d906401bb4a64c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69eef7cb34de5ee0d8f7165e7872c29a.png)
您最近一年使用:0次
23-24高一上·广东深圳·期中
名校
4 . 已知函数
的图像过点
.
(1)求实数
的值;
(2)判断函数的奇偶性并证明.
(3)求证:函数
在
上是减函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acce899605cc4c8f3edd448d3698dbff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ce2f5e22175e3ff8ab5e0afca58f9c.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断函数的奇偶性并证明.
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ce82779a834a6871c96515eaaa5571.png)
您最近一年使用:0次
5 . 已知函数
.
(1)求值:
;
(2)判断函数
的单调性,并证明你的结论:
(3)求证
有且仅有两个零点
并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fa6ff2da8a574faf67845f2fd7d175.png)
(1)求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b131cd4ae45391fd439693590dc8d0.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
您最近一年使用:0次
名校
解题方法
6 . 定义在R上的函数
,当
,且对任意
,有
.
(1)求证:对任意
,都有
;
(2)判断
在R上的单调性,并用定义证明;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84302e08e2e09d2d62548d35e6a40288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885000d706e589a10515ff0d93cae55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db7387dec34f24cacb1cd95c433e8a4.png)
(1)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6d0da3cbcaa04a639eaac12c0e29d1.png)
您最近一年使用:0次
2017-02-08更新
|
1129次组卷
|
2卷引用:河南省周口市周口恒大中学2024届高三上学期期中数学试题
名校
解题方法
7 . 已知函数
,
.
(1)求证:函数
为偶函数;
(2)集合
,
,若
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff9681471371af6e3d0934caee1004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae0b568852a9f688a5fabbe0a1431e9.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5afc8e60a90bef6c1977838238ae42bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ffa75321cd16a9f52bde1bcef2983f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
您最近一年使用:0次
解题方法
8 . 设函数
的定义域是
,对于任意实数
,恒有
,且当
时,
.
(1)求证:
,且当
时,有
;
(2)判断
在
上的单调性;
(3)试举出一个满足条件的函数
,并说明举例的理由.
![](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/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac82501b461d044f78e7ae5b86cd3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5456d544e2f8d22c08f3ccee002dad4a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)试举出一个满足条件的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
9 . 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)
您最近一年使用:0次
名校
10 . 已知函数
且
.
(1)求证:
为定值,并求该定值;
(2)设函数
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a01ceda3d93a97534cf2e6c3bfb4dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7297210ecc4a06625860ef4215b42f7.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83e2a1bbfbb16d630ceb03e446901ce.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3141a4cbf5e3e12ccca84f2d0427430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次