已知函数
和
分别为奇函数和偶函数,且
.
(1)求函数
的解析式,并判断该函数的单调性(不须证明);
(2)解关于
的不等式
;
(3)判断方程
是否有根?如果有根,请求出该根所在的一个长度为
的区间
;如果没有,请说明理由?(注:区间
的长度
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefc6cf085a1ef5a957907b1cd2ef9e5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1234a0ffb906a1d5ba57828c4df22b.png)
(3)判断方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f459a9b8184912cbf87b550803e21f40.png)
更新时间:2022-12-08 12:30:22
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解答题-问答题
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名校
解题方法
【推荐1】已知函数
是偶函数,
是奇函数.
(1)求实数
的值;
(2)若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edba9d657afc1b921b6a626b6b9c4bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b598239ee8f938eda6d1281944efe81.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7955baa98437b38e2f0e45c8bdae1538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】已知函数y=f(x)
(a,b,c∈R,a>0,b>0)是奇函数,当x>0时,f(x)有最小值2,其中b∈N,且f(1)<
.
(1)试求函数f(x)的解析式;
(2)问函数f(x)图象上是否存在关于点(1,0)对称的两点,若存在,求出点的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4648b55828fae47d758a4f9d62a785e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
(1)试求函数f(x)的解析式;
(2)问函数f(x)图象上是否存在关于点(1,0)对称的两点,若存在,求出点的坐标;若不存在,说明理由.
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名校
解题方法
【推荐1】已知函数
.
(1)若函数
为奇函数,求实数
的值;
(2)求函数
的值域;
(3)求函数
的单调区间;
(4)若关于
的不等式
的解集
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fa3d1f6c418c27e89ff30430f7b0e9.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0117fc237a59fcc07a45d8bfbb9b8468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f177814752ff64f02a988c4bffe80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
【推荐2】已知函数
.
(1)设函数
在区间
上的最小值为
,求
的表达式;
(2)设函数
,若对任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39378b5561de2c8f74cf5d2bcf84b154.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d31e98e14496175347b1b9b5452701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4169c5f606352788872a03fe5476fea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bdf40b933a90257d0e6adbddcf8838a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐1】已知
.
(1)当
时,
时,求
的取值范围;
(2)对任意
,且
,有
,求
的取值范围;
(3)
,
的最小值为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad48963a0d010c75896624436186214.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a495c197fcbacb8c109aa0060525a371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99f6241f03f76761403af0c53d3a0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18366c5d28d28abb643838e1e69310a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8814438b8affe65eba614d3bc4d528c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
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解题方法
【推荐2】已知定义在区间
上的函数
满足
,且当
时,
.
(Ⅰ)求
的值;
(Ⅱ)判断
的单调性并予以证明;
(Ⅲ)若
解不等式
.
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/fbf158a779784c97beecc533269f6649.png)
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/1303bb2fa5694d9aa0315d2c403ade35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1ab9e519ac8d08860625da32238906.png)
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/181340d8b4934870a5bc0d5047df68ea.png)
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/db96825ddda74ce29006deb5d39e630e.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/e507e65b48844e69b8d1775392d05a29.png)
(Ⅱ)判断
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/1303bb2fa5694d9aa0315d2c403ade35.png)
(Ⅲ)若
![](https://img.xkw.com/dksih/QBM/2015/11/19/1572299368153088/1572299374477312/STEM/8969ac5641d1486f937ba7d12dede948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db6cbc410d287b2e9f33204af408137.png)
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解题方法
【推荐3】已知函数
.
(1)判断函数
的奇偶性,并给出证明;
(2)解不等式:
;
(3)若函数
在
上单调递减,比较
与
的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4216c3b0840bcb7c7a846bfb21e25e3e.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b7cefc80bf9f008c8781268d973227.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5fcdbaa94998546f6242568ae4ed56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e962d20b233fe25af2157a5b142c7e30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc08c112b18684641d54dbdb8a7446c3.png)
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【推荐1】已知函数
.(其中
为自然对数的底数)
(1)若
,且
在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d94e5edc48a908e96404888ec8cc32b.png)
上是增函数,求
的最小值;
(2)设
,若对任意
、
恒有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1a82e0e52290142699609a11afbe80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d94e5edc48a908e96404888ec8cc32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabd5c9c1361ad20509b12efe296612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e782457ec0edfb09c01da0c26ec6710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0abcf89a8fd5fb00b25bfe32f29b06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】张同学在函数章节学习中遇到过许多形形色色的函数,其中有很多函数的形态是具有共性的,于是张同学提出了下面2个猜想,请同学们选择下面的任意一个问题回答或反驳张同学的猜想.
(1)已知函数
的零点是
的零点是
,证明:
.
(2)已知函数
的零点是
,证明:
.
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb113c900e07d80fdcd8afed691b54b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfe04161d6ebd5964979d54faef5c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f700e9e84ec901bf75313a29757740fa.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a1cb7e36c08e6f1822258f65f2865e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6829485c1d817b5eed2e1a81ed0b642d.png)
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