解题方法
1 . 已知
是奇函数.
(1)求
的值;
(2)若
,
①证明:
在区间
上单调递增;
②写出
的单调区间(不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6794b9b34ac23dc91f77f307b4b0cf4c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc57f6764a1952b8e39d2463fe2ba153.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
②写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 对于给定的抛物线
,使得实数p、q满足
.
(1)若
,求证:抛物线
与x轴有交点.
(2)证明:抛物线
的最大值大于等于抛物线
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d972cf8c74b5218298b60908716a8d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c059fce1db054ebb94902a84d25fcd43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e864b9d4b6a0aa76416348778b26d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2630d6cf14b3e8c82ee7080799901b8d.png)
(2)证明:抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bee92cd110cd46e04633e18c17c4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188f03bd3b6ee375cbc88926cfbcd774.png)
您最近一年使用:0次
3 . 已知函数
,
.
(1)若
,求证:函数
恰有一个负零点;(用图象法证明不给分)
(2)若函数
恰有三个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3638497287cc083c36e43d2b6dadd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0be94f180326e59227954582541ffbe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad013a5114a39844e492f807246dc56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-02-23更新
|
179次组卷
|
2卷引用:湖南省五市十校2019-2020学年高一上学期第一次联考数学试题B卷
名校
解题方法
4 . 如果存在非零常数
,对于函数
定义域上的任意
,都有
成立,那么称函数为“
函数”.
(Ⅰ)若
,
,试判断函数
和
是否是“
函数”?若是,请证明:若不是,主说明理由:
(Ⅱ)求证:若
是单调函数,则它是“
函数”;
(Ⅲ)若函数
是“
函数”,求实数
满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae5a1f884023d902fca242b3490a922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b43b9ac168348257cf8436046eb107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19e893159870d911d83af4f4b2b70ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74314814cdc6fb803abb4692458af131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
(Ⅱ)求证:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6dd0e5f0398c7a86d8fee82d0cc170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
(Ⅲ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498d16aa0037412cb18fa2411610ca2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 对于定义域为[0,1])的函数f(x),如果同时满足以下三条:①对任意的x∈[0,1],总有f(x)≥0;②f (1)=1;③若x1≥0,x2≥0,x1+x2≤1,都有f(x1+x2)≥f(x1)+f(x2)成立,则称函数f(x)为理想函数.
(1)判断函数g(x)=2x﹣1(x∈[0,1])是否为理想函数,并予以证明;
(2)若函数f(x)为理想函数,假定存在x0∈[0,1],使得f(x0)∈[0,1],且f(f(x0))=x0,求证f(x0)=x0.
(1)判断函数g(x)=2x﹣1(x∈[0,1])是否为理想函数,并予以证明;
(2)若函数f(x)为理想函数,假定存在x0∈[0,1],使得f(x0)∈[0,1],且f(f(x0))=x0,求证f(x0)=x0.
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6 . 证明:已知函数
是二次函数,且
,
.
(1)求
的解析式;
(2)求证
在区间
上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b178d7a6c9e31c319407708df1cbce42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2647808a86e7d83b56d7efcdac8a33f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dcdd87d593df4a5c5e98d47fe1cfa6.png)
您最近一年使用:0次
名校
7 . 已知函数
.
(1)求证:函数
为奇函数;
(2)用定义证明:函数
在
上是增函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3fd09aa6bd2c73f713869a28e38e30.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
您最近一年使用:0次
2020-01-19更新
|
335次组卷
|
3卷引用:【全国百强校】青海省西宁市第四高级中学2018-2019学年高一上学期第三次(12月)月考数学试题
【全国百强校】青海省西宁市第四高级中学2018-2019学年高一上学期第三次(12月)月考数学试题海南省临高县临高中学2019-2020学年高一上学期期末数学试题(已下线)3.2函数的基本性质-2020-2021学年新教材名师导学导练高中数学必修第一册(人教A版)
名校
解题方法
8 . 已知函数
的定义域为区间
,若对于
内任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5ea1b2590630b4468e9b73daca2f7a.png)
成立,则称函数
是区间
的“
函数”.
(1)判断函数
(
)是否是“
函数”?说明理由;
(2)已知
,求证:函数
(
)是“
函数”;
(3)设函数
是
,(
)上的“
函数”,
,且存在
使得
,试探讨函数
在区间
上零点个数,并用图象作出简要的说明(结果不需要证明).
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a5572bfcdb0a4905bf670613266a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5ea1b2590630b4468e9b73daca2f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db8805cda07838d256165991623acca.png)
![](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/0cb9ad1e34877b0db02d0219332b0f7b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84518e68c9e73dee93a8a3cafce4d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fa87a940e5467f0f5d2fec0cd3ddd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64cf0a7460760a6993e26d4590058cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33aa094296dbf59fcd88588ad86d434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
您最近一年使用:0次
名校
9 . 已知集合
是满足下列性质的函数
的全体:存在实数
,对于定义域内的任意
,均有
成立,称数对
为函数
的“伴随数对”.
(1)判断函数
是否属于集合
,并说明理由;
(2)试证明:假设
为定义在
上的函数,且
,若其“伴随数对”
满足
,求证:
恒成立;
(3)若函数
,求满足条件的函数
的所有“伴随数对”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7a1aed6c7bf5ad8dc6a9c4071e14e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ac5983ac1b8ead75c11f8022018ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e58703cf57935d56d4b26cf7102811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)试证明:假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e74920f57028200604c2691c8f0fb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e58703cf57935d56d4b26cf7102811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c9ebe3b38d02c837131394d2c32e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86eff5761f61a20c240a428f2a7ceda.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1155e2804263dca432e07cbfea0ffd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
在区间
上的最大值为
,最小值为
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
;
(1)求实数
、
的值;
(2)若不等式
对任意
恒成立,求实数
的范围;
(3)对于定义在
上的函数
,设
,
,用任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
将
划分为
个小区间,其中
,若存在一个常数
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
恒成立,则称函数
为
上的有界变差函数;
①试证明函数
是在
上的有界变差函数,并求出
的最小值;
②写出
是在
上的有界变差函数的一个充分条件,使上述结论成为其特例;(不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a248e47163191168a1b363937eebd618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3210274e57cc0487a58b99ea274b8aa1.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c5e6b1cf8b9ace30d26f232da3dac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)对于定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc272934625d1232ad34eedc6b23267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752c287b0680a053e18be60f6e34ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1b6d5c6b222d95759ea7d39f0b908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b09511efe31176effed50209b4aa5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fc2920f7b5d960d1a927fed29b6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
①试证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
您最近一年使用:0次
2020-01-07更新
|
446次组卷
|
2卷引用:上海市控江中学2016-2017学年高三上学期第一次月考数学试题