20-21高一上·江西南昌·期中
名校
解题方法
1 . 已知函数
,当
时,恒有
.当
时,
.
(1)求证:
是奇函数;
(2)判断并证明函数
的单调性;
(3)是否存在m,使
对于任意
恒成立?若存在,求出实数m的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)是否存在m,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dfb6774881be39c0ba5fd4927d7acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
您最近一年使用:0次
20-21高一上·江西南昌·阶段练习
名校
2 . 知函数
的定义域是R,对任意实数x,y,均有
,且
时,
.
(1)判断
的奇偶性,并证明;
(2)证明:
在R上是增函数;
(3)若
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff2144d6e1b26db35e9d3309e615573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a88b3625a63e21e1114ecd5707927a7.png)
您最近一年使用:0次
名校
3 . 已知函数
是定义在R上的函数,若对于任意
,都有
,且
时,有.
.
(1)判断函数的奇偶性;
(2)判断函数
在R上是增函数,还是减函数,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)判断函数的奇偶性;
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
4 . 已知函数
的定义域为
,且对任意
,都有
.且当
时,
恒成立,
.
(1)证明:函数
是
上的减函数;
(2)证明:函数
是奇函数;
(3)试求函数
在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320cba4d29e050a7e9f4e3b24bdbbc86.png)
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057db09504e1a3e62cd7fc678a7c31ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3fbdfad1c022bc2e07a7befef76dccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7fde71807463dbdfd8fce1655a5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe826b10d86a9d42b7da2c708393efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c76a5d1e06ab2527e67d62d103dc45.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)试求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320cba4d29e050a7e9f4e3b24bdbbc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55706696b67a79d5f6720ffd4996695b.png)
您最近一年使用:0次