名校
1 . 已知函数
,
,
.
(1)当
时,判断函数
的奇偶性并证明;
(2)当
且
时,利用函数单调性的定义证明函数
在
上单调递增;
(3)求证:当
且
时,方程
在
内有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc9b1b321520eae2bf944a9c85c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99caed81bfb141d6e7dac8f6fe9db069.png)
您最近一年使用:0次
名校
2 . 定义在上的函数
满足对于任意实数
,
都有
,且当
时,
,
.
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5850426712b921e7c18b9a9a43712cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e4772345fae89140e5f807b767d54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83eb571b807483dec3599c2fee3b437b.png)
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3 . 已知函数
是定义在R上的奇函数.
(1)求实数a的值:
(2)判断函数
在区间
上的单调性,并用定义证明;
(3)若
有两个零点,请写出k的范围(直接写出结论即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102d64844ddcb9b7e3d0960477ea8d25.png)
(1)求实数a的值:
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b26aea4ce992ee86939c3fc7be97ee7.png)
您最近一年使用:0次
2024-02-05更新
|
384次组卷
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2卷引用:北京市顺义区2023-2024学年高一上学期期末质量监测数学试卷
解题方法
4 . 已知
是定义在
上的奇函数,当
时
.
(1)求
的解析式;
(2)根据定义证明
在
上单调递减,并指出
在定义域内的单调性;
(3)若对任意的
,不等式
恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b0126f3c5830bdba570e5398d07a7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc44426437d3610fe7212db3ac12230f.png)
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5 . 已知函数
,
.
(1)求证:
为偶函数;
(2)设
,判断
的单调性,并用单调性定义加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf688908975687a9bead59e017acacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4741b2cc342a055aefb2d825e45ce77e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae37cac299cbe3ccac181b2175287f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
6 . 已知函数
.
(1)判断函数
的奇偶性,并证明你的结论;
(2)用函数单调性定义证明:函数
在
上是减函数;
(3)写出函数
的值域(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d389b78f753622d6ed895eff86c8e59b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用函数单调性定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
解题方法
7 . 设函数
.
(1)当
时,求
的值;
(2)判断
在区间
上的单调性,并用函数单调性的定义证明你的结论;
(3)当
时,
的最小值为3,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9088a940f6c06449d4fed2d29d3b56dd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-01-20更新
|
220次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
名校
8 . 已知函数
.请从条件①、条件②这两个条件中选择一个作为已知,解答下面的问题.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答记分.
(1)求实数k的值;
(2)设函数
,判断函数
在区间
上的单调性,并给出证明;
(3)设函数
,指出函数
在区间
上的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f7d13f97baaeb36f1785d09d389f0c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a38b1e7496745c92fabb36b1c5d6f16.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b3d8321b8a85830c2af2ead9f36867.png)
注:如果选择条件①和条件②分别解答,按第一个解答记分.
(1)求实数k的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d825ec419a668aa8efb06d43d3c2a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f4afb555297200a8cbc59a428ed8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
您最近一年使用:0次
2024-01-17更新
|
369次组卷
|
5卷引用:北京市海淀区2023-2024学年高一上学期期末考试数学试题
名校
9 . 定义在
上的函数
满足对于任意实数
,
都有
,且当
时,
,
.
(1)判断
的奇偶性并证明;
(2)判断
的单调性并证明;
(3)解关于
的不等式
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91288f3376f00e3e4e37376c14f5c81d.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5482a9055030f833a8ad7a1988ec72e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e94d2ce192a26b34f53a1b1a17d631.png)
您最近一年使用:0次
名校
解题方法
10 . 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
|
338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