1 . 已知函数
且
过定点
,且点
在函数
的图象上.
(1)求函数
的解析式;
(2)若定义在
上的函数
恰有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbc41ba647a7774b168ca21ed05ee9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03373ea8b1ba832b962fca109769ec4f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5f4dd21b7cb605a33c565b40fb9898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
2 . 已知
是一元二次方程
的两个不同实数根.
(1)是否存在实数
,使
成立?若存在,求出
的值;若不存在,请说明理由;
(2)求使
的值为整数的实数
的整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a4dfe122cd5fcd036a01aaa35c351e.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e56b53ccb80592b122c78b0ccbd9ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f0741b1180d12b3ec31c1d4afe0328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 设函数
的定义域为D,若
同时满足①
在D内为单调函数,②存在区间
,使
在
上的值域也为
,则称
为闭函数.
(1)若
为闭函数,求k的值;
(2)已知p为整数,且
在
上为闭函数,求p的最小值以及p取到最小值时t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bd3dd7705fa6e441d2dd9ae496d87e.png)
(2)已知p为整数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e60c0180864fa0231e88a8bc9c4be1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17bec7c34bd729548e08554fb2d60a.png)
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