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解题方法
1 . 函数
的一个零点所在的区间是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5170b47edad85891636137f00debfd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-22更新
|
761次组卷
|
5卷引用:北京市汉德三维集团2024届高三下学期第二次联考数学试题
北京市汉德三维集团2024届高三下学期第二次联考数学试题(已下线)模块二 类型5 思维漏洞类12个易错高频考点广东省湛江市第一中学2024届高三第二次大考数学试题(已下线)函数-综合测试卷A卷(已下线)第07讲 函数与方程(十一大题型)(讲义)-1
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解题方法
2 . 已知函数
,且
.
(1)求
的值;
(2)判断
在
上的单调性,并用定义证明.
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227faad8de9d704d712aea5b39de1a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf2e72d1393c790b353484f13f581cc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af12d927649df46e96635fe5e6b9dc4.png)
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2024-04-12更新
|
344次组卷
|
2卷引用:北京市八一学校2023-2024学年高一上学期12月月考数学试卷
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3 . 计算:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7218aa36f90dc46d1004daa396de2b.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7218aa36f90dc46d1004daa396de2b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b42011f840f47d21f9ae7f9d5834488.png)
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名校
解题方法
4 . 已知函数
,下列区间中含有
零点的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66cc30d6c142a589d7372313ed1c7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 对于集合
,定义函数
.对于两个集合
,定义集合
.已知集合
.
(1)求
与
的值;
(2)用列举法写出集合
;
(3)用
表示有限集合
所包含元素的个数.已知集合
是正整数集的子集,求
的最小值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2599ffc8c40e388d718a3c743a513d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc1230fe52b22fe2047caf0ff1fad9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76693f0b722f0adbb55b35a64703256b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03e23c5f50122bd65c621c69f301f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf3030d12212582bfe4c35826833fd0.png)
(2)用列举法写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e37e656d05244fe3a5769cd1446725.png)
(3)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a58429b36d406ab944c4b1b04a2fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884a76f27d8958f920bbe4dd7be24e5b.png)
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6 . 已知函数
.
(1)求函数
的定义域.
(2)判断函数
的奇偶性,并说明理由.
(3)对
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793db9e1eb2d025813b3c2fbc5efc337.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56198272df2de178f893dcb1b0a711c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 集合
由有限个实数组成,定义集合
的离距
如下:实数轴上,集合
中的每个实数
对应一个点
,实数
对应的点
与所有这些点
的距离的算术平均数记为
,称函数
的最小值为集合
的离距,记为
.例如,集合
的离距是0,集合
的离距是2.
(1)分别求出集合
的离距;
(2)求数集
的离距;
(3)已知非空数集
满足
,试写出一个关于
的大小关系的等式或不等式,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e51c8010a4568d7d44f261973dea420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39412925212a989c503e891db840609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
(1)分别求出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384a3e8b9a7ffb00bb124ba97b7c992.png)
(2)求数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22accc2928d3370f48a84cc4703a4b07.png)
(3)已知非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e6c4bb62b14f8e70d8f8b1ac911bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3598ab9c4ac9a9496c5f34b9b5fda3cf.png)
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名校
解题方法
8 . 已知函数
的定义域为
,其图象关于原点对称.当
时,
.
(1)求函数
的解析式.
(2)求不等式
的解集
.
(3)设函数
其中
的定义域为集合
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2e0bb6d63b7bcaee92a470d58cc399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725ff4f383f8eeb3a9ed216a538c1e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d591386a9942d6dae60e156eeaec67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b05d2be27e8f53e4de3071846dffb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 在不考虑空气阻力的条件下,火箭的最大速度
(单位:
与燃料的质量
(单位:
),火箭(除燃料外)的质量
(单位:
)的函数关系是
.当燃料质量与火箭质量的比值为
时,火箭的最大速度可达到
.若要使火箭的最大速度达到
,则燃料质量与火箭质量的比值应为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a951688a79345aedea9e992237990e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f7c4a8558eff6427d22b6c0c855721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f7c4a8558eff6427d22b6c0c855721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c3f33428c8f9b7bf447475c5ed0036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf05ae039c8848423a4245cbdc9436a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6760574fc868808787a2bb268fd8404.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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