名校
1 . 已知函数
,函数
.
(1)写出函数
的增区间;
(2)若命题:“
”为真命题,求实数m的取值范围;
(3)是否存在实数m,使函数
在
上的最大值为0?如果存在,求出实数m所有的值,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585dcceddb1b3d07043f5ce8870f1ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabbf9e7b54d06ae9eaa6352a8e38b3b.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若命题:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589eae88a3915b7cb886e2120d4f027a.png)
(3)是否存在实数m,使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea515e1d30beee9434b8c61f077868f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
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名校
2 . 对数函数
(
且
)和指数函数
(
且
)互为反函数.已知函数
,其反函数为
.
(1)若函数
定义域为
,求实数
的取值范围.
(2)若
为定义在
上的奇函数,且
时,
.求
的解析式.
(3)定义在
上的函数
,如果满足:对任意的
,存在常数
,都有
成立,则称函数
是
上的有界函数,其中
为函数
的上界.若函数
,当
时,探究函数
在
上是否存在上界
,若存在求出
的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84518e68c9e73dee93a8a3cafce4d26.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/3d76ee3b131ecd6aa1aacf7fb7b3eb15.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/246de316aacce5e2a1b482840ff02f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925c788c10bb1694aff18e1cdb998713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15341a333e7a119d1a96fd0949882b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
(3)定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c4c6cfc4b6d863bbded8d1a1a8de7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1224a557188a0141c20df6749ace6c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9415ab7474c0b9e1227feeea97fee3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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