1 . (1)计算:
;
(2)已知
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9465189da1b5eeeca14745444cb2e9a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f40502a43bb02f09cbd31230a0293ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce243be426caee3afd136c7c47f3e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8fc3e1f16ed24264dcfc7f606cac62.png)
您最近一年使用:0次
2021-01-25更新
|
858次组卷
|
2卷引用:江苏省南京市2020-2021学年高一上学期期末数学试题
解题方法
2 . 已知定义在
上的函数
是奇函数.
(1)求函数
的解析式;
(2)判断
的单调性,并用单调性定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b613b6b500b84dc3110164e7a794c235.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2021-03-23更新
|
239次组卷
|
2卷引用:江苏省南通市如东县2021-2022学年高一上学期期末数学试题
名校
解题方法
3 . 对于等式
(
,
),如果将a视为自变量x,b视为常数,c为关于a(即x)的函数,记为y,那么
是幂函数;如果将a视为常数,b视为自变量x,c为关于b(即x)的函数,记为y,那么
是指数函数;如果将a视为常数,c视为自变量x,b为关于c(即x)的函数,记为y,那么
是对数函数.事实上,由这个等式还可以得到更多的函数模型.如果c为常数e(e为自然对数的底),将a视为自变量x(
,
),则b为x的函数,记为y,那么
,记将y表示成x的函数为
.
![](https://img.xkw.com/dksih/QBM/2020/12/18/2616851596918784/2618798317150208/STEM/dbeba9e6-5ad3-49ec-bec1-c8b0df3602f0.png)
(1)求函数
的解析式,并作出其图象;
(2)若
且均不等于1,且满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcfe7bb3f607ac047d70fea54a21aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce04612f2dc7928760c86f67a883df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f3e12dc69463d61f935db6ee063558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2020/12/18/2616851596918784/2618798317150208/STEM/dbeba9e6-5ad3-49ec-bec1-c8b0df3602f0.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48b7f21ec39e043bc83387c42f9f089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a94bd7ccb598e5da3338b22f0cb2d2.png)
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2020-12-21更新
|
327次组卷
|
2卷引用:江苏省百校联考2020-2021学年高一上学期第二次考试数学试题
名校
解题方法
4 . 已知函数
为奇函数.
(Ⅰ)求实数m的值;
(Ⅱ)判定函数
在定义域内的单调性,并用定义证明;
(Ⅲ)设
,
,求实数n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1582f40a1aa7d3530301198264f88e6.png)
(Ⅰ)求实数m的值;
(Ⅱ)判定函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58559a19d92aebb47ca32dbce7a42b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7d7bd7701e0359b33437923c7b052c.png)
您最近一年使用:0次
2021-01-29更新
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452次组卷
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2卷引用:江苏省盐城市上冈高级中学、龙冈中学等2020-2021学年高一上学期期末数学试题
名校
5 . 若定义在R上的函数
满足:
,
,都有
成立,且当
时,
.
(1)求证:
为奇函数;
(2)求证:
为
上的增函数;
(3)若
,且
,
,
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9c7ce3315926725a1583323ec15875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857e07c5fb7f2410d6d267a00889db10.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5485dbf2af203775f17c47d00595c3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f832d9cca2d5c9d76d38374e2a258d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9e7a4af65844b19fd5d5a71017eaf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2b3de4cf642f247a9aa1cb56f57f51.png)
您最近一年使用:0次
2020-11-21更新
|
474次组卷
|
3卷引用:江苏省连云港市2022-2023学年高一上学期期末模拟数学试题(5)
江苏省连云港市2022-2023学年高一上学期期末模拟数学试题(5)长春市东北师大附中2020-2021学年上学期期中试卷高一数学试题(已下线)练习11+抽象函数性质专题专题-2020-2021学年【补习教材·寒假作业】高一数学(北师大版)
名校
解题方法
6 . 已知函数
(
,
).
(1)求函数
的定义域;
(2)证明:
为偶函数;
(3)求关于
的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea65ba82103734982249590cf85a6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ca573da13035f8b5a176322297f3f0.png)
您最近一年使用:0次
2021-01-28更新
|
1167次组卷
|
3卷引用:江苏省徐州市2020-2021学年高一上学期期末数学试题
解题方法
7 . 已知函数
.
(1)判断并证明函数
的奇偶性:
(2)用定义证明函数
在
上为减函数:
(3)已知
,且
,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b636844dddba5c8e2a96f34e03c7eddb.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba8d2141d285c963ec078fe2ce8686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46722475cf1caa3c9979a457040790ba.png)
您最近一年使用:0次
解题方法
8 . 已知函数
为奇函数.
(1)求
的值;
(2)判断函数
的单调性,并用单调性定义加以证明;
(3)解关于
的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db04bee3cf15e611c7d075e94c81f3c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128b1efa9db440dc419cfa129d7e9044.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
中,
.
(1)
中是否必有一个内角为钝角,说明理由.
(2)若
同时满足下列四个条件中的三个:①
;②
;③
;④
.请证明使得
存在的这三个条件仅有一组,写出这组条件并求出b的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f4e1a51292d9fe2c89ee23771f92d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07fcfd5d22629a729e21052aafc2fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf7e7beb7ca1ffd445c7501bd5e3dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413f9851aad373d782ae62b308f1de85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2021-01-21更新
|
699次组卷
|
7卷引用:江苏省盐城中学2021届高三下学期第一次模拟考试数学试题
解题方法
10 . 已知二次函数
.
(1)
、
为整数且
,若函数
在区间
上单调递增.
①求
、
的值;
②函数
,已知在区间
上函数
的图象恒在
图象的上方,求实数
的取值范围;
(2)函数
在区间
上是否存在零点,请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccb2dd21b357c360211dca7e4c4723e.png)
(1)
![](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/5698bc3ee0746f8b39cb2494860536a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d6d1a0f888cf196ef7cd1d5506af7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
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