解题方法
1 . 定义在区间
上的函数
满足:若对任意
,
,都有
,则称
是
上的上凸函数.
(1)判断函数
是否为上凸函数?为什么?
(2)若函数
在
上是上凸函数,求
的取值范围;
(3)在(2)的条件下,当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063223b5d1fc1b45ad67c449b330a064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e349f49908801a73999320f7a49820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a80f796352ce199941b79b4aeffa3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
2 . 函数
的定义域为
,满足:①
在
内是单调函数;②存在
,使得
在
上的值域为
,那么就称函数
为“优美函数”,若函数
是“优美函数”,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3cbbd6af2784dc00e271ace3d4e885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6408971212257f3dd7e05ecbf6f77451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12ad42a40c1c2207ed387ff3d828f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
满足
且
为奇函数.
(1)求
的值;
(2)判断
在区间
上的单调性;
(3)当
时,若对于任意的
,总有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6c326cc9d98fe43a1ef99174ec5101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d660b2fbb91d3877318b3ecb18ef5446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a6c3b8663fc8274d946cec4b5bfbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
解题方法
4 . 已知非空集合
,函数
的定义域为
,若对任意
且
,不等式
恒成立,则称函数
具有
性质.
(1)当
,判断
、
是否具有
性质;
(2)当
,
,
,若函数具有
性质,求正数
的取值范围;
(3)当
,
,若
为整数集且具有
性质的函数均为常值函数,求所有符合条件的
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd2491dc0189bacbcb09d74ee95e9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8a1b0b32229f6a9f5b85c11f05bee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6e6e1fc1d8667992ce119e79bb8bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20380b0bd02fec0e125d73d3fc6f202b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88621b319f851a0b59e98f903efc1de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199ec3824d5faac7eeec10f97c05b3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa3fb6bdded6d83b90d4852f5af85e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20bfa0755dee91480f6a893ca71c230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aaad488867733390ad7d5024e808107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20aef71c8785b2d87f78e8e3fb79ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a1f8ed373823d79f44edbef03e1984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
5 . 设
,
的范围是D,则函数
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca883d4eea9c9050631a1b31d3faad85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f11702dad2d3204ae56294509742ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74856f5f4d464ff00b415faf10e1a076.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 设非空实数集
中存在最大元素
和最小元素
,记
.
(1)已知
,
,且
,求实数
.
(2)设
,
,是否存在实数
,使得
?若存在,求出所有满足条件的实数
,若不存在说明理由.
(3)设
,函数
在区间
上值域记为
,若对任意
,函数都满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc6d063c729ead63517594e355600a8.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4ab0a21457d9bda0c4c2920846ed4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870016ae8c86ab9743ea08abe8524b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab45f61b9961397eb1c6c467a7526d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c6dfc58e55c7542b4164feb1280ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8bacb6f4dbd204504f1299a443e0d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad986dfa21d3289298ba469baaf6552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46aad39c3617bc635aec113d2ec52bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaca9c1dac608a386df1848e8459ce9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb848c2e3353bcb126d14fed803fe2a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7562646285aeb2167c2734b4d2fdf91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 设函数
是定义在
上的函数,若存在
,使得
在
上单调递增,在
上单调递减,则称
为
上的单峰函数,
称为峰点,
称为含峰区间.
(1)判断下列函数中,哪些是
上的单峰函数?若是,指出峰点;若不是,说出原因:
①
,②
;
(2)若函数
是区间
上的单峰函数,证明:对任意的
,
,若
,则
为含峰区间;若
,则
为含峰区间;
(3)若函数
是区间
上的单峰函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e953a254e24b408dfcecffac161580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
(1)判断下列函数中,哪些是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06aa7e8049fd1144ed3eed08023832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f8c7c55e8bb8b490e374041df9f338.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01b424cd6859d55f2e1ba4c80d2c8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ce40da2cbd52723210bbfa98a7f81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14283f108568721e6d9ec8d42036be33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba30f1aa5e75750c67b142fc1d7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a570f0086433e604736679f7192c3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffcdf84c6476c0d046035d49d423287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b2e67cd10ebbced3d964ab0dc5c298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
8 . 已知函数
是奇函数(
,且
).
(1)求
的值;
(2)若
时,
的值域为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1a4fa622dcfa9d561ea48fdf085a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f107318d3ccad8ac914daf37c36bc72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 已知函数
(其中
,
且
)的图象关于原点对称.
(1)求
,
的值;
(2)当
时,
①判断
在区间
上的单调性(只写出结论即可);
②关于
的方程
在区间
上有两个不同的解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12154418066b2425ef585f853c01723c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acbcee94702048585e7bbb9515433cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fce155963060b2e5b9147a185897cc.png)
②关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09fc27a1ec1a964e08090b8d9dbd490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637860c9ff749cd15012879c3ee66365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-03-10更新
|
2215次组卷
|
8卷引用:上海市南洋模范中学2022-2023学年高一上学期期末数学试题
名校
10 . 对于函数
,若存在区间
,使得
,则称函数
为“可等域函数”,区间A为函数的一个“可等域区间”.给出下列四个函数:①
;②
;③
;④
.其中存在唯一“可等域区间”的“可等域函数”的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8381052ba6db8323837b1db33549be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f591c9cc5a83b749eac9e7664c2eadb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ace0c072dc6426e620c02a26c892b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7630110d5583d6f49a4c7fb2e597db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d8688735f2938e31046550247c48cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e93bd8ef567c91cbbc38ac78ed23f7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-01-14更新
|
516次组卷
|
2卷引用:上海市曹杨二中2016-2017学年高一上学期期末数学试题