2023高一上·上海·专题练习
1 . 下列函数中,哪些是对数函数?
(1)
;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980a4e54f218bbeecb6aa0caf97dbb5c.png)
(3)
;
(4)
;
(5)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969f2f61631def143fb4ab8918ce08fc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980a4e54f218bbeecb6aa0caf97dbb5c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a8e6b7a717962cc1064a8f239229ab.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193395e28ccacb43c9d69e8da62dd17a.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8458f29d7376c0c6c5437fc5615c8d.png)
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解题方法
2 . 已知函数
,其中
,记
,且函数
是偶函数.
(1)求函数
的表达式:
(2)若不等式
在区间
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43745e8daea75b38cab51bcea8026cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ea36101bd7f0cefa20125125903e0e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c335aadabdbf03c7125e4c90062e8b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabac9f69a121b9fe969c7b3fe721b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
3 . 如果函数
满足以下两个条件,我们就称
为
型函数.
①对任意的
,总有
;
② 当
时,总有
成立.
(1)记
,求证:
为
型函数;
(2)设
,记
,若
是
型函数,求
的取值范围;
(3)是否存在
型函数
满足:对于任意的
,都存在
,使得等式
成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
② 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdccde6a17dc78bec232630577f99d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d5873aa225a83805e1072ef8119b7a.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc540d6c4de05039557cdfe8c78ceeec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54428f4829c8061f79df9f492305c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951b05c96af4f7704de24ac541b3f172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb679de6747c1a9147225d7b61c436f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe0c952b97016a6816cfca66e024ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdc6e6a0e6584bea7deb91b0841fa28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe8e17429b079c4965fae3bef4e6b25.png)
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2024-01-10更新
|
419次组卷
|
2卷引用:上海市静安区2024届高三上学期期末教学质量调研数学试题
解题方法
4 . 已知函数
.
(1)当
时,求该函数的值域;
(2)若
对于
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ee55add803bf1b64b580d078cae20b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0a85351d1433071b7e7bd11eaaba85.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb48cabb2ca42afe6e3e3d09db6385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3368388525e30cb7179909b03184eb.png)
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解题方法
5 . 已知
.
(1)解不等式
;
(2)判断函数
在其定义域上的单调性,并严格证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d94accdb1056c6c03b1fc33deed162.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2e0bb6d63b7bcaee92a470d58cc399.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff26491b344566f7bb04cbb7deb6baa1.png)
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6 . 已知集合
,
.
(1)求A和B;
(2)若
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2134320794b4ab7cf0a06ede8ea1188c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157846d30363de5d37d49b60e8753a13.png)
(1)求A和B;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc88d8e6c706fca06d9740a804bbab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07241606934d6c75cf04455979d0e1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知幂的基本不等式:当
,
时,
.请利用此基本不等式解决下列相关问题:
(1)当
,
时,求
的取值范围;
(2)当
,
时,求证:
;
(3)利用(2)证明对数函数的单调性:当
时,对数函数
在
上是严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e0630a1632f6368fb824ebfdead0d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca16bee4a8ecee60c31f9aaac02539b0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27eb687fdf1568ab06ce8119845823c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92098b3da769963a2320cf1d8dad00a.png)
(3)利用(2)证明对数函数的单调性:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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2023高一上·上海·专题练习
解题方法
8 . 解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f8cd6cfe2ec2fc39992c4280ac7fb4.png)
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2023高一上·上海·专题练习
解题方法
9 . 解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c3403a1c209ee923ee695abf10e3e1.png)
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名校
解题方法
10 . 已知函数
是定义在R上的奇函数,当
时,
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e52bcd642c5b65842f866fea48ca164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
您最近一年使用:0次