已知函数
,
是定义在
上的奇函数,且当
时,
,当
时,
.
(1)若
成立,求x的取值范围;
(2)求
在区间
上的解析式,并写出
的单调区间(不必证明);
(3)若对任意实数x,不等式
恒成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f52f6ee8ead43c46f73102b87a2d943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e99bebf8db0d314aacb2cb1f09bf48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8f84f5de5d5fe7a643ddfb4ee243eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd7a1f45776fc5187e58c34fe8e5b57.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e873199423f079755d2eedd6bbb2ed7e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1417a39c99b1e6b489c7c033a0625af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若对任意实数x,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970435d69524445676210d51a5dffa07.png)
更新时间:2022-03-26 15:43:08
|
相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】已知函数
,
,其中
,设
.
(1)如果
为奇函数,求实数
、
满足的条件;
(2)在(1)的条件下,若函数
在区间
上为增函数,求
的取值范围;
(3)若对任意的
恒有
成立.证明:当
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac18d45cf62862e456a5757bd81f6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cc01dd0de04563061deb6c90fdce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90e1dc4714287648d0bebcac913ded7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026694a3e840b4e1d706e70f4ed4d0c5.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)在(1)的条件下,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27e0400d730672ae2110ff48786dd1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0cc678e10b051d9392f03460b35a49.png)
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较难
(0.4)
【推荐2】已知函数
.
(1)用定义证明
是偶函数;
(2)用定义证明
在
上是减函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1439c562a1331c7245f7ad4c70e0b6b3.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c0c037867665979b6dc75fb995f9ec.png)
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解答题-问答题
|
较难
(0.4)
名校
【推荐1】(1)已知关于
的方程
有两个不等的根
,
(
),求
的值
(2)已知
,
,直线
:
与函数
的图象从左至右交于
,
,直线
:
与函数
的图象从左至右交于点
,
,记线段
和
在
轴上的投影长度分别为
,
,当
变化时,求
的最小值.
(3)对
,
,是否存在实数
,使对任意的
,关于
的方程
在区间
上总有3个不等的根
,
,
?若存在,求实数
与
的范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38abfe94aab2620c3f39e483615dfbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb20586cda25e2255bf1aba5c6cf2c32.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f13e7902be1ccf0469a89094a4ebc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923c953fe8d1cbe98f78eec7eb0491a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b1923dfc8a50b0a5ce1e5a8adfc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923c953fe8d1cbe98f78eec7eb0491a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76e6299e98e6fdbe7fe3f9d46e08519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c68b5e5d935be4762fa35be0f29a9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86bc584ad930b670e2e46cf1173d4995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2fa47c66eb6fb98623d006cc61fb8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2253c1a391344579ceeac505910c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8477ed6c4d8c19638a0c21edb8a3d4d.png)
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解答题-问答题
|
较难
(0.4)
名校
【推荐2】已知
,
.
(1)若
,求
的取值范围;
(2)若函数
恰有两个零点,求实数a的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b39c5d66018f0736a0457961c91e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a1141aa62d95fc3b75e3d6833aaaf0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a3f237b03aaa5f0fb96e572706349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a3c49d8680218bdcc2f39f2b4f601.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08180ea9d4238fd449255a0b47f3bb2f.png)
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解答题-证明题
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较难
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名校
【推荐1】已知函数
,
为常数.
(1)证明:
的图象关于直线
对称.
(2)设
在
上有两个零点
,
.
(ⅰ)求
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d572266d7847c48bf451ea5a81a56ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6400ec27a77d671d1fcc1d883d525dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d036114de7d006d748ca6bb0af07d8e.png)
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较难
(0.4)
【推荐2】已知函数
的图像与直线
两相邻交点之间的距离为
,且图像关于
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f38849d01b93c5a5e8ed82d316e4904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f56a20bc5fce6b02217627b42249854.png)
(1) 求的解析式;
(2) 先将函数的图象向左平移
个单位,再将图像上所有横坐标伸长到原来的
倍,得到函数
的图象.求
的单调递增区间以及
的
取值范围.
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较难
(0.4)
【推荐3】已知函数
,(
是自然对数的底数)
(1)求
的单调递减区间;
(2)记
,若
,求
在
上的零点个数.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776fa6439168522f352d683994355658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00210f79b04a8f6bc1922433d00bc89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d0ee7b8d3fa2c655c90a05c6b52338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791d941a68f38eab62db8ea91c051a37.png)
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|
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名校
解题方法
【推荐1】设
为正整数,已知函数
.
(1)判断函数
的单调性,并用定义证明;
(2)求关于x不等式
的解集;
(3)若函数
在区间
单调递减,比较
与
的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2553714b94b412f4b2ff53f5264df9.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求关于x不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f524fd74bb5c67ccff0ce2c5c795f9d.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe816176c28c1838f35fe865ec0ec0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63dbe55b675c440885a0dab98ed43a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
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较难
(0.4)
名校
解题方法
【推荐2】已知函数
是奇函数.
(1)求a的值,判断
的单调性并说明理由;
(2)若对任意的
,不等式
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5855fb0d5b9f7b4f6bd3c8828f3be6.png)
(1)求a的值,判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7d2bb9fd6de312a742ef10c81b9b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4427891d473403dd0a31adb99339f2d.png)
您最近一年使用:0次