请仔细阅读以下材料:
已知
是定义在
上的单调递增函数.
求证:命题“设
,若
,则
”是真命题.
证明:因为
,由
得
.
又因为
是定义在
上的单调递增函数,
于是有
. ①
同理有
. ②
由①+ ②得
.
故,命题“设
,若
,则
”是真命题.
请针对以上阅读材料中的
,解答以下问题:
(1)试用命题的等价性证明:“设
,若
,则:
”是真命题;
(2)解关于
的不等式
(其中
).
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
求证:命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
证明:因为
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/8e1dba6af48b4f02a02353cfceac54bc.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
于是有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/e138ae2d9d174247aa79ca4be523361f.png)
同理有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/6e01071f3f38469e8e15c3d76700b775.png)
由①+ ②得
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
故,命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
请针对以上阅读材料中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试用命题的等价性证明:“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36ce14a18f423fcff11def7512150e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4c9d254df7fc5169fe8e745a3b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c0c6e3ada0970f9a1fefd7200ff677.png)
更新时间:2019-01-30 18:14:09
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