1 . 对于函数
及实数m,若存在
,使得
,则称函数
与
具有“m关联”性质.
(1)若
与
具有“m关联”性质,求m的取值范围;
(2)已知
,
为定义在
上的奇函数,且满足;
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有“4关联”性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf557bc0501acbf300fd4ae5993b7242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4870a0f8fee7a8357094ab4309263752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e1ce7071be0743ded4a087fd908eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96101eb5dce02c0213ad008413f3066.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263b718b5b3cbc27f3e0ef94f4157f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db64040b2fa9d65075b41ada928fa6.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c839f85fe048ed0882889e22f5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2c5422d4b9f8c11a5ad1b62c6bb87.png)
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2024-01-24更新
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