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1 . 给出下列四个选项中,其中正确的选项有( )
A.若角![]() ![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.设角![]() ![]() |
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9卷引用:福建省三明市第二中学2022届高三10月阶段(一)考试数学试题
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2 . 已知函数
.
(1)判断函数
在其定义域上的单调性(不需要证明)﹔
(2)对任意的
,都有
,若存在
的两个取值
,使得
为常数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bff5eeeb9414192fe13fe7fa5599864.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c995d957e9e95c66544e876318641d5c.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0044f2840ab023ee12a23f6d88dadf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38a915d8585180f3731ece24e3cf995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1579867c6de8346ee8fb115b2fa0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb561b71047c16ab4354be0e4653359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d52943e3995bdda062b3f7930265682.png)
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4卷引用:四川省成都市蓉城名校联盟2021-2022学年高一上学期期中联考数学试题
3 . 已知函数
,
,定义函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec09e7ab26188617083f3b467231250.png)
(1)设函数
,
,求函数
的值域;
(2)设函数
(
,
为实常数),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445f5ea3b5f3ccc852c66a4b27d3b95f.png)
,当
时,恒有
,求实常数
的取值范围;
(3)定义区间
的长度为
,已知
,
,
,
为常数,设
,
为实数,
,且
,
,若
,求
在区间
上的单调递增区间的长度和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70458945dae62f8f6a553dfaa8eb723a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b40b099989abb2d15ddf60413c8a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec09e7ab26188617083f3b467231250.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed94bc7970736b3f07ac833b851a751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3027ab2bb54feb0d186d776b27d500b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6d073f26c136e2d862e11a8494c3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22af653d3aa1a75dc6de30a1cfb6cea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445f5ea3b5f3ccc852c66a4b27d3b95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07180028d2769a3fb9735853912d4a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22af653d3aa1a75dc6de30a1cfb6cea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8c97a77335a5dc082b1e99154eee37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de607dcc8133a2a3c0fa5aeaa8e841e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9694a88c6ecf60f398dfb5c6e2745009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13222360e2133bb0594c52215ed32d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
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