1 . 已知幂函数
是定义在R上的偶函数.
(1)求函数
的解析式;
(2)当
时,求函数
的最值,并求对应的自变量
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c52a591bfc43ba69abc2822bfe5f19b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a142f28e90c952e0e29b88ab01722c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83d040e2b0b6e04d8c27037e77af382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2 . 若函数
为幂函数,且在
单调递减.
(1)求实数
的值;
(2)若函数
,且
,
(ⅰ)写出函数
的单调性,无需证明;
(ⅱ)求使不等式
成立的实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4363e72db9ff107cc9088b9d2a2685be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b2c2c021798d9cad33114fdaa98540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
(ⅰ)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(ⅱ)求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14b4f9432ad82e5ecc9e2a4d16d0e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
3 . 已知幂函数
(
)为偶函数,且在
上单调递减.
(1)求
和
的值;
(2)求满足
的实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d00201d277325ec1bda73a757f237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32701e66e47ee38a59363479eaa8aa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知幂函数
为偶函数.
(1)求
的解析式;
(2)若
在
上是单调函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af87fdae52a19c1fa2707d95558fb5b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06befffb4e80b1503a2678d269a9dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知幂函数
的图象关于原点对称.
(1)求实数m的值;
(2)设
,(
且
),若不等式
对任意
恒成立,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfad69280555ca5f9aa904496b924ffb.png)
(1)求实数m的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f87b41eab59a0f9807c01a6d7e5e840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa38ca27c6c0c40d5e36b2ae4fb7ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
您最近一年使用:0次
名校
解题方法
6 . 已知幂函数
在
上单调递减.
(1)求
的解析式;
(2)若
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d1a602f47cc3b563fa9e3885e5734b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1fef9bc2a9cbff032abcfe1fa91615e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
7 . 已知幂函数
为偶函数,
.
(1)求
的解析式;
(2)若
对于
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484a7b3614f4676d2665591a3a556f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006f7132f69e255de73b518cef076be9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32db32bcbd565870f5966a91a8acc1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
解题方法
8 . 已知幂函数
为偶函数.
(1)求函数
的解析式;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac95bc5361303cfdab45647a5c2daf11.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a117da268eb3135604c1aa232f3b253.png)
您最近一年使用:0次
名校
9 . 已知幂函数
的图象过点
.
(1)求实数m的值;
(2)设函数
,用单调性的定义证明:
在
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f569b808afe234c32b84358c7279027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b597e27f847c60634025b38fca66d.png)
(1)求实数m的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf62f4b1e2094352ae6c922c8f68e76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
您最近一年使用:0次
2024-01-31更新
|
205次组卷
|
3卷引用:安徽省阜阳市2023-2024学年高一上学期期末联考数学试卷
解题方法
10 . 已知幂函数
的图象关于
轴对称.
(1)求
的值及函数
的解析式;
(2)设函数
,求
在区间
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4768b67151a484e59222fa2d8bd13559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7221d6342dbde71d7408e0e0b63af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
您最近一年使用:0次