1 . 小颖同学在学习探究活动中,定义了一种运等“
”:对于任意实数a,b,都有
,通过研究发现新运算满足交换律:
.小颖提出了两个猜想:
,
,
,①
;②
.
(1)请你任选其中一个猜想,判断其正确与否,若正确,进行证明;若错误,请说明理由;(注:两个猜想都判断、证明或说明理由,仅按第一解答给分)
(2)设
且
,
,当
时,若函数
在区间
上的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4235fe8a6cf0446dbf476822b6dbbce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7ff4ffa27279dbf509cfb852446813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525c1a68848e95e6b419e0bbec3c0957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b648347b0e5ed2bdc821dc7cf50d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8d87094a7c50f062fa23902cd23c20.png)
(1)请你任选其中一个猜想,判断其正确与否,若正确,进行证明;若错误,请说明理由;(注:两个猜想都判断、证明或说明理由,仅按第一解答给分)
(2)设
![](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/9d386474416a278ca29be6075fa076d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49910fc853928999a0acbcc67f4c295c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733c4ee92975bec9a52b9b2d544d790f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a964eadb835069b591f479b7c67e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-11更新
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2卷引用:福建省莆田市莆田第一中学2023-2024学年高一上学期期末考试数学试题