对于函数
,称
为函数的“特征数对”,同时称
为
的“特征函数”,记
的特征函数为
;
(1)求函数
的特征数对;
(2)若
的图象向左平移
个单位长度,得到
的图象,解关于
的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c6f29b2b1955715616003d51d8b77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900bc64b3de2dd45bc9cccef611350fb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad36bb51b4bf20b99a03ffc065c8446.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3255893ecb77d5ad6613d07a02531a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebd1d359040a1172a944ded96ed0127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1298896f2be12bfc3346563d07451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a003183bae02ff873169e5d74d485c.png)
更新时间:2019-12-13 20:27:30
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相似题推荐
解答题-问答题
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解题方法
【推荐1】设
,函数
,
.
(1)讨论函数
的零点个数;
(2)若函数
有两个零点
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b30db1d4f4a2cf9b2e7c0224468b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5c9dd749202f50f605cc804bedbe1f.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](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/c571dcdb66f1c91cea2a9e889da3622d.png)
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【推荐2】设函数
(
且
,
).
(1)若
是定义在R上的偶函数,求实数k的值;
(2)若
,对任意的
,不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bef6b1f23bdd37d46331b69103eb764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7306ed239acc7afb3e64e857a7b557e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0618947d2ea889486de6c8e038c587.png)
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【推荐1】已知向量
,
,函数
.
(1)求
的最小正周期及
图象的对称轴方程;
(2)若先将
的图象上每个点纵坐标不变,横坐标变为原来的2倍,然后再向左平移
个单位长度得到函数
的图象,求函数
在区间
内的所有零点之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6a439ddba8174280a963fa3b9a6515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbb0a10ca98d0857a7e517624e456db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d79201a7a170cd6f3661042c6e0a9e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若先将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d497d0f3acdfa9a4146e76bab7798c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb70e56cab5c2a4a7175b0d0dc1d1ea.png)
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【推荐2】已知函数
为奇函数,且
图象的相邻两对称轴间的距离为
.
(1)求
的解析式.
(2)求
的最大值.
(3)将函数
的图象向右平移
个单位长度,再把横坐标缩小为原来的
(纵坐标变),得到函数
的图象,当
时,求函数
的值域.
(4)对于第(3)问中的函数
,记方程
在
上的根从小到依次为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
,试确定
的值,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e779bb3629cf50ef93131ad378365494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fd7f56bae242ab9961e4d5d942e4f9.png)
(3)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30df565ea4b03c3ab0124d155b54965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(4)对于第(3)问中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c40363783d0e33e6a40e68957391ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca46524e23ce781f3f2410cc3863a6a6.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf143ca6acd9bafcce6716f4e6f2d9a3.png)
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【推荐1】为迎接2020年奥运会,某商家计划设计一圆形图标,内部有一“杠铃形图案”(如图阴影部分),圆的半径为1米,
,
是圆的直径,
,
在弦
上,
,
在弦
上,圆心
是矩形
的中心,若
米,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/75e9bac9-9908-4abe-be9e-2375cbf51612.png?resizew=182)
(1)当
时,求“杠铃形图案”的面积;
(2)求“杠铃形图案”的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9204b815291b41cd4e99d1aa358f543d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297f91f8de05cd18a6053b675836d59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7269957476be59967a7879bf011fe2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/75e9bac9-9908-4abe-be9e-2375cbf51612.png?resizew=182)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
(2)求“杠铃形图案”的面积的最小值.
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【推荐2】某景区拟将一半径为
的半圆形绿地改建为等腰梯形
(如图,其中
为圆心,点
在半圆上)的放养观赏鱼的鱼池,周围四边建成观鱼长廊(宽度忽略不计).设
,鱼池面积为
(单位:
).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/6ca14eb4-291e-403e-8eff-f89d56d761a3.png?resizew=139)
(1)求S关于
的函数表达式,并求鱼池面积何时最大;
(2)已知鱼池造价为每平方米2000元,长廊造价为每米3000元,问此次改建的最高造价不超过多少?(取
计算)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3eb9b39420dfcf48e341125d8b629a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11db4b9921a9fe4d5c03b17bafc852fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d7b4bb12628d5ed455d814b8aafa1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/6ca14eb4-291e-403e-8eff-f89d56d761a3.png?resizew=139)
(1)求S关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)已知鱼池造价为每平方米2000元,长廊造价为每米3000元,问此次改建的最高造价不超过多少?(取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a7ff6bb8000946da9599d7d903ac9a.png)
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