已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/876c84ad-77b1-4f08-8b8c-a5174ae1103d.png?resizew=200)
(1)求实数
的值,并在所给的平面直角坐标系中画出函数
的图象;
(2)根据
的图象写出
的单调区间,并求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cea8945d5e644abb0ab1cefac4ed858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2dec9053c9d6608fa34b48afc23d04.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/876c84ad-77b1-4f08-8b8c-a5174ae1103d.png?resizew=200)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
更新时间:2019-11-27 22:30:02
|
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适中
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【推荐1】已知函数f(x)=-x2-2x,g(x)=![](https://img.xkw.com/dksih/QBM/2018/8/1/2030704095854592/2038060944424960/STEM/fb3819acb6df4c0cb29dec2c2d363ddd.png?resizew=82)
(1)求g[f(1)]的值;
(2)若方程g[f(x)]-a=0有4个实数根,求实数a的取值范围.
![](https://img.xkw.com/dksih/QBM/2018/8/1/2030704095854592/2038060944424960/STEM/fb3819acb6df4c0cb29dec2c2d363ddd.png?resizew=82)
(1)求g[f(1)]的值;
(2)若方程g[f(x)]-a=0有4个实数根,求实数a的取值范围.
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适中
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名校
解题方法
【推荐2】设函数
(
,
为实数),
.
(1)若
,且对任意实数
均有
成立,求
表达式;
(2)在(1)的条件下,当
时,
是单调函数,求
的取值范围
(3)设
,
且
,
且
为奇函数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de122801dfb31da6b933c90f3b98087f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5d0b0af83e25d925687063047cb27c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431537df789febf4bc45e3dc23cefaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ce93b9f0ea8d7e3a5e4a4f2fcacf45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3838d126e7480e3e0827999f3cf9f771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1218eda19f74a1ed50ab106265c6621f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75d9b18ccb3f9743b7c2dbe1e8d8c73.png)
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解答题-证明题
|
适中
(0.65)
【推荐1】已知函数
(其中
),且
,
.
(1)求
,
的值;
(2)求
的单调区间;
(3)若正实数
,
满足
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64527c19df5c1d45128d4d26c4a886be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1d97c42f236c05bd0f97ee6538ea61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b49cf13331c53446d9082db8734157.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d900314efb0e4cacb6e5de945b5397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
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适中
(0.65)
解题方法
【推荐2】已知奇函数y=f(x)定义域是R,当x≥0时,f(x)=x(1-x).
(1)求出函数y=f(x)的解析式;
(2)写出函数y=f(x)的单调递增区间.(不用证明,只需直接写出递增区间即可)
(1)求出函数y=f(x)的解析式;
(2)写出函数y=f(x)的单调递增区间.(不用证明,只需直接写出递增区间即可)
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解答题-证明题
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适中
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【推荐1】已知函数
,令
.
(1)求函数
的值域;
(2)任取定义域内的5个自变量,根据要求计算并填表;观察表中数据间的关系,猜想一个等式并给予证明;
(3)如图,已知
在区间
的图像,请据此在该坐标系中补全函数
在定义域内的图像,并在同一坐标系中作出函数
的图像. 请说明你的作图依据.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49e790b1d37f231c10c6c93facc372c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc186db32143695b72cfa3818d28793.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)任取定义域内的5个自变量,根据要求计算并填表;观察表中数据间的关系,猜想一个等式并给予证明;
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![]() | … |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9589f0f76da55001a64079a8143dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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解答题-证明题
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适中
(0.65)
【推荐2】已知函数
,且
.
(1)判断并证明函数
在其定义域上的奇偶性.
(2)证明函数
在
上是增函数.
(3)画出
在
上的图象,并求在
上值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35fc4a430ac9cc0cc23a051d915c70a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6855784817151468771f29c0fc38fc9.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
(3)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7fefece0cf6660a409832f72dff95.png)
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