解题方法
1 . 已知函数
对任意实数
、
都满足
,且
,以下结论正确的有( )
![](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/c92e0efc4bb9daf1e30cd4aaa2dd5ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
2 . 已知函数
的定义域为R,对任意实数
,
满足
,且
,当
时,
.给出以下结论:①
;②
;③
为R上的减函数;④
为奇函数. 其中正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/657221948689bc58b72ec871eb1ea1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f451fefd1e370de85a57d30d76fac6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a039b83b7784132b820a32c9894a2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac65ef4b5cdd7370c09f20ec9e59f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c432487864c0f12100e46f20f7f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b2e8e9a0d7febf73fc557adf3f7806.png)
A.①②④ | B.①② | C.①③ | D.①④ |
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解题方法
3 . 已知函数
满足:对
,都有
,且当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b0337b2d14c529ae61d4fd9a975459.png)
函数
.
(1)求实数
的值,并写出函数
在区间
的零点
无需证明
;
(2)函数
,
,是否存在实数
,使得
恒成立?若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c68e603ad17bf72634d2cc6d785ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20111317cfd9de576cb594063b92acb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b0337b2d14c529ae61d4fd9a975459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c08d1b45ecee648f2f745884c0874.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b7c2420c387be8882df4359ac10b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788273681f22dd4f097e90c5de1821e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5cee84381134d1937627d7b4eff6308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de535172010550ecee49cfcbfd752897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . 已知函数
(其中
),若关于
的方程
有四个不等的实数根,从小到大依次为
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8fc90b6273d8bc253c113ec2c2e1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2492929137a56abbdeeea4101a4b896a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知函数
是定义域为
的偶函数,当
时,
,若关于x的方程
,有且只有7个不同实数根,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb05b8c65151650eaecbad638e509c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800cb5a9b29276bfca97608d4b94ef03.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 已知函数
,若函数
有三个零点a,b,c,且
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbd4c07833d1282c1606681bb156d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92abc7642e3db7f9d6a51ff85c84ff30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb3fa21842ca6421d3c85eddb7f7b6f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知函数
,假如存在实数
,使得
对任意的实数
恒成立,称
满足性质
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3992d93b8257ca1c354b4c47d7e7afb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26376c11e57ebc6e98780d8fe466cf9e.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
8 . 已知
,函数
,
.
(1)若
,
,求
;
(2)若
,
,求m;
(3)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8913c4863ff7e4060e075f79f9e2a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2476c6a7b73d4d8ad99ffaca4afb76d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73b85378c1f65d0ca0e4c30a14ccee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302b4d220b829aeede0b874ac26c35f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a83eb8584e1ab069a24ea3911778c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb00c0bbee9e93f495c57a6805b447f5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51d3fb60fdba2bc8bd0811fcabfa3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82f4ce319a1e1ff7137e0267201ea27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e067be545a0178382625422a2e67621d.png)
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名校
解题方法
9 . 设函数
的定义域为
,
为奇函数,
为偶函数,当
时,
.若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe17821ea81c6fec60bd5273901bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25990e1d373ac30d7480633e47cc1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b9205cf6a58cf9f9fcaab3417519f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de52485227217f25d11676b289fa5c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdff65ed9e7a2ca957f420c40a3a4cb0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-17更新
|
400次组卷
|
2卷引用:安徽省A10联盟2023-2024学年高一上学期期末检测数学试卷
10 . 函数
.
(1)求
和
的值,判断
的单调性并用定义加以证明;
(2)设
是函数
的一个零点,当
时,
,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aff5cf0dcc110cf6e02bbe27667e4bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b530377e3fe56b7988935dd73d9dccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665696c68051b2a8881f767d10f80fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2ea3741c5ced38436180d4ba8e2256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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