1 . 对于函数f(x),g(x),φ(x)如查存在实数a,b使得φ(x)=a•f(x)+b•g(x),那么称φ(x)为f(x),g(x)的线性组合函数,如对于f(x)=x+1,g(x)=x2+2x,φ(x)=2﹣x2存在a=2,b=﹣1使得φ(x)=2f(x)=g(x),此时φ(x)就是f(x),g(x)的线性组合函数.
(Ⅰ)设f(x)=x2+1,g(x)=x2﹣x,φ(x)=x2﹣2x+3,试判断φ(x)是否为f(x),g(x)的线性组合函数?关说明理由;
(Ⅱ)设f(x)=log2x,g(x)=log
x,a=2,b=1,线性组合函数为φ(x),若不等式3φ2(x)﹣2φ(x)+m<0在x∈[
,4]上有解,求实数m的取值范围;
(Ⅲ)设f(x)=x,g(x)=
(1≤x≤9),取a=1,b>0,线性组合函数φ(x)使φ(x)≥b恒成立,求b的取值范围,(可利用函数y=x+
(常数k>0)在(0,
]上是减函数,在[
,+∞)上是增函数)
(Ⅰ)设f(x)=x2+1,g(x)=x2﹣x,φ(x)=x2﹣2x+3,试判断φ(x)是否为f(x),g(x)的线性组合函数?关说明理由;
(Ⅱ)设f(x)=log2x,g(x)=log
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/d1b92c8f530a447aaa4cb203f70e2d5c.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/13ccb5c1dc27472fb55f7c2ad2e2ebc7.png)
(Ⅲ)设f(x)=x,g(x)=
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/d46d5079b6a8452e911f1effa835de73.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/a8eb09afb3eb45209bb572043cb71eea.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/4df8737c8234456c9d635177399c2f99.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572557944938496/1572557950500864/STEM/4df8737c8234456c9d635177399c2f99.png)
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2 . 已知函数
.
(1)若
,求函数
在区间
上的值域;
(2)若函数
在区间
上有最小值3,求
的值.
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/0bdd60613702452d8f5a3d9db8a6f468.png)
(1)若
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/01e3ac8da3754be389be23ecd108df4f.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/d8bfc88a06b74c318307d45a00e80c51.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/a60de4b707254c9e8dc3cdba61a83152.png)
(2)若函数
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/d8bfc88a06b74c318307d45a00e80c51.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/284e55cdaefb46578bae8d68540cc29d.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163676057600/STEM/0cc8f30b1d8b443093197671370421eb.png)
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3 . 已知函数
在区间
上是增函数,则
的取值范围是
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163675738112/STEM/e921f43b77e3466f8c8427fd345ccbbb.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163675738112/STEM/ef6bc6bdbaaa488e8197b25ad1e085d4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/21/1573163669700608/1573163675738112/STEM/d72b866c7c334db88cba1fbec6ba61b0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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