解题方法
1 . 若闭区间
满足:①函数
在
上单调;②函数
在
上的值域为
,
,则称区间
为函数
的
次方膨胀区间. 函数
的2次方膨胀区间为_____________ ;若函数
存在4次方膨胀区间,则
的取值范围是_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91393ddcf411f513b77caad29a31cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6724c68c4206bd95683998d800f7f676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a993d222157197c263ae4a8255228a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c4821d3e69fbb6a1f8d0afe0d725f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
2 . 设
且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4e857897b5a9f64308cf5906b9fa13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f63ff6daf204a5c9441f5ea82686910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
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3 . 已知函数
的定义域为D,若存在区间
使得函数
满足:
①函数
在区间
上是严格增函数或严格减函数;
②函数
,
的值域是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bc2c22621c164294428fee27b961c4.png)
,
则称区间
为函数
的“n倍区间”.
(1)判断下列函数是否存在“2倍区间”(不需要说明理由);
①
; ②
;
(2)证明:函数
不存在“n倍区间”;
(3)证明:当有理数
满足
时,对于任意n
,函数
都存在“n倍区间”,并求函数
和
所有的“10倍区间”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e207cf62e3a7e282eac4c4a3455bbf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bc2c22621c164294428fee27b961c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda1b32a2ac436a267e47c9ccb621e1f.png)
则称区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)判断下列函数是否存在“2倍区间”(不需要说明理由);
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b78b98443d32512ddcfe86aefd507db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028f5145fad99aa994b09c8ef698e2d2.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175da291995b66f7a5e4e770062fbaba.png)
(3)证明:当有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ecbfedde46d325dbbe88c139436923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda1b32a2ac436a267e47c9ccb621e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da668452bf94a7df60422815ae3b3d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e87b5d998252950639557ec2b8946d0.png)
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4 . 已知
是奇函数,定义域为
,当
时,
,当函数
有3个零点时,则实数t的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfd684344fb9708260ce900b0746e4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29145ea38299ebe4c2424013b73e2043.png)
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5 . 设函数
的定义域为I,如果存在区间
,使得
在区间
上是单调函数且值域为
,那么称
在区间
上具有性质P.
(1)分别判断函数
和
在区间
上是否具有性质P;(不需要解答过程)
(2)若函数
在区间
上具有性质P,
(i)求实数a的取值范围;
(ii)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2866a347edffa2be486d2d76b2eb7eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12959f65e9db83c446c35d3261a33171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda16bdd2671a8e299a0d9c00504202d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a147de2fe3443ea0c982efad1beb7f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
(i)求实数a的取值范围;
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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2021-01-21更新
|
488次组卷
|
2卷引用:北京市丰台区2020-2021学年度高一上学期期末练习数学试题
2019高三·江苏·专题练习
6 . 函数f(x)=(m2-m-1)
是幂函数,对任意的x1,x2∈(0,+∞),且x1≠x2,满足
>0,若a,b∈R,且a+b>0,则f(a)+f(b)的值:
①恒大于0;②恒小于0;③等于0;④无法判断.
上述结论正确的是________ (填序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac3753083d165869654318ceb6fbceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bbaa673d75c93089cadc45bef573db.png)
①恒大于0;②恒小于0;③等于0;④无法判断.
上述结论正确的是
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