名校
1 . 设全集为
,定义域为
的函数
是关于x的函数“函数组”,当n取
中不同的数值时可以得到不同的函数.例如:定义域为
的函数
,当
时,有
若存在非空集合
满足当且仅当
时,函数
在
上存在零点,则称
是
上的“跳跃函数”.
(1)设
,若函数
是
上的“跳跃函数”,求集合
;
(2)设
,若不存在集合
使
为
上的“跳跃函数”,求所有满足条件的集合
的并集;
(3)设
,
为
上的“跳跃函数”,
.已知
,且对任意正整数n,均有
.
(i)证明:
;
(ii)求实数
的最大值,使得对于任意
,均有
的零点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2425552313d50a253bfb3cb4e9974ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182856db60fa5cfda34c97b5748197a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d18ae300954e363c2637120f4f3ef82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e77ed55488688257efc354fad8875c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c853fd24a33bd11fbf2d5dba50806d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108abe0b3ee27e7549f6cc0d86c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946552f0f9f048a916879402e4d315a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47efc68941a3be03f5bebbabfbe388fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e94f0ab8e7418164e0c7481150e6b5.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d80a81e375bf3c3bdc3603ef7a2a37.png)
(ii)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fbab6e1a7963d26e1265e1686cba40.png)
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解题方法
2 . 若实数
满足
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905487a2a54ec22ac51e56de4fe76c26.png)
A.![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
2024-02-21更新
|
852次组卷
|
3卷引用:专题6 学科素养与综合问题(多选题11)
名校
3 . 设函数
且
表示不超过实数
的最大整数,则函数
的值域是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50feaef0c83d6e46b5ba77688bb838d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755ea37c1ebdbdc49b92196b129e8b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aea51d290a3460f405bb04a6e6c1a67.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
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4 . 已知集合
.给定一个函数
,定义集合
,若
对任意的
成立,则称该函数
具有性质“
”.给出下列函数:①
;②
;③
;④
其中具有性质“
”的函数的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5d1aa4cc6d7420da507e3f32808d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0500974fa4ff5245dc7516e96410d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e847907fda445c04edd732d1b77acc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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解题方法
5 . 若函数
与
满足:对任意的
,总存在唯一的
,使
成立,则称
是
在区间
上的“
阶伴随函数”;当
时,则称
为区间
上的“
阶自伴函数”,
(1)判断
是否为区间
上的“2阶自伴函数”?并说明理由;
(2)若函数
为区间
上的“1阶自伴函数”,求
的值;
(3)若
是
在区间
上的“2阶伴随函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41286a1ca05dc551a9f734e6ed89996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd330acca8e17f5ff9aca1f0f312df50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58547687c14a41680e0a429ae79c757d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ed4089763bb5e9c6cb838d6391a173.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970193f414f7f52993b9f6cbabb77a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8d6ad7aa09c9c5f552a4c8e867a6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697b5e0d89c89ea58ae14982046e86c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b6d3b74c1697e4efd1dd7181d2ea39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知函数
的定义域为
,若存在实数
,使得对于任意
都存在
满足
,则称函数
为“自均值函数”.
(1)判断函数
是否为“自均值函数”,并说明理由;
(2)若函数
,
为“自均值函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f57537b1a7ca7e4eed38a922ac707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c52f32cce9d825753cecdb287f4745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4f647724654e761774d92b838d224a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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2023-10-19更新
|
662次组卷
|
5卷引用:模块二 专题2 函数 单元检测篇 B提升卷
(已下线)模块二 专题2 函数 单元检测篇 B提升卷辽宁省沈阳市东北育才学校2023-2024学年高三上学期10月联合考试数学试题(已下线)专题05 三角函数4-2024年高一数学寒假作业单元合订本福建师范大学附属中学2023-2024学年高一上学期期末考试数学试题北京市延庆区2022-2023学年高一下学期期中考试数学试题
名校
解题方法
7 . 定义
,设函数
,若
使得
成立,则实数a的取值范围为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817d37255f06adad9b6995724f5bc56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561a80c738da59af31406fb14ea43895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccd7af9298cd5ff19d8866fedb42ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-05-26更新
|
1003次组卷
|
3卷引用:专题03 函数导数简单应用(六大题型)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)
(已下线)专题03 函数导数简单应用(六大题型)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)广东省广州市天河区2023届高三三模数学试题天津市重点校2022-2023学年高二下学期期末联考数学试题
2023·广东广州·模拟预测
名校
解题方法
8 . 函数
是定义在R上的奇函数,当
时,
,则函数
在
上的所有零点之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b808a0c73d88d7ebe7ffeb023743e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba8ae3e7d73cd70135e6e3d366b8672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0656a62ca479cbc2ec613f9e88dc65c4.png)
A.-32 | B.32 | C.16 | D.8 |
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9 . 若函数
满足:对于任意正数s、t,都有
,
,
,则称函数
为“L函数”.
(1)试判断函数
是否是“L函数”;
(2)若函数
为“L函数”,求实数a的取值范围;
(3)若函数
为“L函数”,且
,求证:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd6668744366fc80aa91e2c7853bbf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23624c379c76dcff423ada0c89083280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0035bf4d1cd0978e745d32536e78cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222db87c8bf85e4548488f09e2d9dfc.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e3cd8564b48c35ba4247b79fe3d9db.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baf957b7b5f8ced7b6330c4f6d92290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e331b120141e088148a6e80b6376d3f2.png)
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解题方法
10 . 已知
,
是定义在
上的增函数,
,若对任意
,
,使得
成立,则称
是
在
上的“追逐函数”.已知
,则下列四个函数中是
在
上的“追逐函数”的是( ).
![](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/5c98f2d5ac32d2fbf4d29cb34941b78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aab23b08a206f2afb86a2d9109a26d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208575de4f7422c995dd601c54d264d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6b462f8734a368277b55a5dc05382a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405741480780f91e6342eaf76b16263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c98f2d5ac32d2fbf4d29cb34941b78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-02-15更新
|
572次组卷
|
3卷引用:第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)
(已下线)第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)江苏省连云港市2022-2023学年高一上学期期末学业质量调研数学试题山西省朔州市怀仁市第一中学校2023-2024学年高一下学期第一次月考数学试题