解题方法
1 . 设
(a为实常数),
与
的图像关于y轴对称.
(1)若函数
为奇函数,求a的取值;
(2)当a=0时,若关于x的方程
有两个不等实根,求m的范围;
(3)当|a|<1时,求方程
的实数根个数,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b9b42638033a93f26cbf4fd89b76ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae905f856b26183ebe83225350df5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110c8d90cd5808b83431c72cdb1976e0.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495d1f17eec7fe720a8fd8840822f55e.png)
(2)当a=0时,若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9405eb72b163ac2b712231899fe398d.png)
(3)当|a|<1时,求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4603bbe40ed845c0fba5dea69053d305.png)
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2 . 已知函数
为
上的增函数,则实数
取值的范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c668078b7026cc5162ba85bade7699f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
3 . 已知函数
,若函数
有四个零点
,
,
,
,且
,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da76c7124256c6c120acdc4552820b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ffeb0ff803530b726bd0258b1ef0f1.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/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
A.![]() ![]() | B.![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2023-01-11更新
|
907次组卷
|
3卷引用:安徽省淮北市第一中学2022-2023学年高一上学期期末数学试题
名校
解题方法
4 . 已知
为定义在
上且周期为5的函数,当
时,
.则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f423993ffbd13fcbe7b2768ff64c37f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ff1b22a5530e6692ea856d5ce9274a.png)
A.![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.方程![]() ![]() |
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名校
5 . 已知关于
的函数
为
上的偶函数,且在区间
上的最大值为10.设
.
(1)求函数
的解析式.
(2)若不等式
在
上恒成立,求实数
的取值范围.
(3)是否存在实数
,使得关于
的方程
有四个不相等的实数根?如果存在,求出实数
的范围,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39a21c80ae3e990027ecea33bfb6424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85564659d145e38c0887d186db1c8573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba94b35258a2fbde34d7e26be524fb6e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e567c3e841ba226b51543b0dc43e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4d001c51cf7b47102f641ded56b01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6544efd3f7cea29d879628d508f0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2020-12-26更新
|
2315次组卷
|
8卷引用:安徽省安庆市第一中学2021-2022学年高一上学期期中数学试题
名校
解题方法
6 . 定义两类新函数:
①若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”;
②若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”.
(1)设函数
的定义域为
,已知
是某一类新函数,试判断
是“
函数”还是“
函数”(不需说明理由),并求此时
的范围;
(2)已知函数
在定义域
上为“
函数”,若存在实数
,使得对任意的
,不等式
都成立,求实数
的取值范围.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/c411a8fd18c8de5c7de91ead2534602b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/c3c98c995fc2687a803998d262d754e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da9ea25accbf7eeb60424224b68c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c918ca5d4e6d46ed130f85e5fa608d.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53275eb34d75ead1b48d1d78123d536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56002ab09438fcb642fde70b10ee9720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94526b73a995b128c50c2487e192f057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2020-08-07更新
|
594次组卷
|
2卷引用:安徽省合肥市第六中学2019-2020学年高一下学期学情检测数学试题
名校
7 . 已知函数
.
(1)当
时,方程
的解的个数;
(2)对任意
时,函数
的图象恒在函数
图象的下方,求
的取值范围;
(3)
在
上单调递增,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd4c1cd356731fb8defe81a11b5b9ee.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7629b32068eceefee92962b82645b6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636e471cf2e1904f72ca6ad4c8f0378a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2016-12-04更新
|
556次组卷
|
3卷引用:安徽省安庆市石化第一中学2016-2017学年高一上学期期中数学试题
解题方法
8 . 已知函数
.
(1)若关于
的不等式
的解集为
,求a,b的值;
(2)已知当
时,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba85cd64b03a571816a2c9beab7f6314.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb9056a484e06d3cd225c7293033d1c.png)
(2)已知当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d6a9ea77300969ca2f356f5606939f.png)
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2024-02-11更新
|
227次组卷
|
2卷引用:安徽省部分重点中学2023-2024学年高一上学期期末测试数学试卷
名校
解题方法
9 . 下列说法正确的是( )
A.若命题![]() ![]() ![]() ![]() ![]() |
B.若不等式![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.定义在![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
10 . 已知函数
可以表示为一个偶函数
和一个奇函数
之和,若关于
的不等式
的解集非空,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855011f492a306c4d357aa2a47ce0377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5898bf37b47e54d71359f9c5a39cd24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次