名校
1 . 已知函数
,
.
(1)求函数
的定义域,判断并证明该函数的单调性;
(2)函数
,若对
,都
,使得
成立,求实数
的取值范围;
(3)函数
,若对
,都存在
,使得
成立,求实数
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4dca84cba2b9ba42de0a54fd3dde4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc6570333ab37b35226ab3574f9bba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bb7bb34b5f4d32fc07b47752fa171d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1276f06af99b4602c0f99ece9c97697c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a86b821f593ab9d43f1f67ffb160c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066e246ae8bffb3e409faed863a40af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bb7bb34b5f4d32fc07b47752fa171d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914bdb6c1d82b8982f219a72d470e47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d968b1d9e98342bf10b32b29dc52fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求证
为偶函数;
(2)当
时,函数
存在零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e5ec10dd5c1e578e1f57e5b6931842.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eceb09ecb20215b3efb0908ea4b5e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
,其中
,
.
(1)证明:
;
(2)若
,求实数
的值;
(3)问是否存在实数
,使得函数
的定义域为
时,其值域恰好为
?若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095897564b2bb696f4cb3e8016b3fa01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70d3d06b06ec518a2d171b62304bccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7b459051885f09735db25862878159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d61c2a73aed7ffff74baa4f0460fb00.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e541585024d5799abc7184aaea52f0b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfe560ec40006cb5f89f54d8e7540ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)问是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa208c8bab34df3e76f87552abc985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f67001e8efa767d4b2a693745bdba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
4 . 设函数
,
,且
,
.
(1)求
的值及
的定义城;
(2)判断
的奇偶性,并给出证明;
(3)求函数
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931ea2b356b28c771ad4a49e919fa76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d74d706d2e4392e25016e9101d07ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
您最近一年使用:0次
2023-09-05更新
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639次组卷
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