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解题方法
1 . 已知对于任意实数
,不等式
恒成立,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcdf620c2395f828b34be292278d046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
2 . 已知幂函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6665b1d0d9f7a8ee9f8511cbab3aa27d.png)
满足:①在区间
上是严格增函数;②函数图像关于原点对称.
(1)求同时满足①②的幂函数
的表达式.
(2)在(1)条件下,
图像先向左平移了2个单位,再向上平移了1个单位,恰好和函数
的图像重合,求函数
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6665b1d0d9f7a8ee9f8511cbab3aa27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca47538388c179dc5847f2ba2bffca92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(1)求同时满足①②的幂函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)在(1)条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
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3 . 已知
是方程
的两个实数根,则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb93fc7782cbff3dc7db980c2a240a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a85ef415d41705027815a818c46f1d.png)
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4 . 已知一元二次不等式
的解集为
,则不等式
的解集为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a1f86b4a5330727015867732ff6a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1c8f0836b1e3ba81f5371855a6365f.png)
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5 . 已知实常数a、b,满足
,
(1)证明:关于
的方程
有两个不同的实数解.
(2)若关于
的方程
有两个不同的实数解
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
(1)证明:关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358677b8b71354b1b639b231e5c647a7.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358677b8b71354b1b639b231e5c647a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b5f32c09caa0be0d4c33be07aa4530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ba253c3d7949e75483437b3dc3841b.png)
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6 . 已知
,则下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-07更新
|
556次组卷
|
2卷引用:上海市新中高级中学2023-2024学年高一上学期期中数学试题
名校
解题方法
7 . 如果函数
的定义域为
,且
恒成立,则函数
的图像关于直线
对称.已知函数 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1603a9f6f5e0617db8a852a1a705e2f.png)
(1)若
,求
的值;
(2)证明:函数
的图像关于
对称;
(3)现在已经得知函数
在
上是严格减函数,在
上是严格增函数,关于
的不等式
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc58a89f281be53f284c0ddb5b7fe828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a454588e9beb97c69a0332a7c5c796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1603a9f6f5e0617db8a852a1a705e2f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(3)现在已经得知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be381da62d4a042476aa11dbd5824e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a76f56568aa5a381aeda448d05476a.png)
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8 . 已知幂函数
的图象关于点
中心对称;
(1)求该幂函数
的解析式;
(2)设函数
,在直角坐标系中做出函数
的图像;
(3)根据
中图像,直接写出不等式
的解集,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3959d58f6fca431496f6158a3c6a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(1)求该幂函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33a5ae399a9fa76c7a3f04615c17083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)根据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd791cdf876b9a9e58f251f803aeb66.png)
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9 . 方程
的解集为____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8365d65fa051a16da0c24f2c9ee558c8.png)
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10 . (1)已知
,用a、b表示
;
(2)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdc428c439bd6742f240a7d542bf293.png)
求b的值;
(3)已知
,试用
表示
;
(4)已知
,试用
表示求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdc804cafca7d7500135f066057a08a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7aebf1a2766eb9b3030102df5443a9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdc428c439bd6742f240a7d542bf293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05e5da5ec7a2d14972118f259bc9e9f.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7baf540910f39fa4f2c1f52909637a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d0c3b5d21faefb2bec8f753d407766.png)
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65873f57f38d08da56b05ff88ff4b0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13aac2585429d9a4d063644e737f629f.png)
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