2021高一上·江苏·专题练习
1 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6230be733604a67c0594ebeb10d14890.png)
(1)若角
的顶点与原点
重合,始边与
轴的非负半轴重合,它的终边过点
,求
的值;
(2)若
,函数
是奇函数,求
的值;
(3)若
,是否存在实数
,使得函数
的最小值为
,如果存在,求出实数
的值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6230be733604a67c0594ebeb10d14890.png)
(1)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9d86d46657a5e186e6a8ed698474c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d7f440c63f1cc2199857b0c6e74ee6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800412cade2e256b1f313603b28587df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9987521a298dc846d8bf70d84e96a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 已知函数
(其中
).
(1)若
,判断函数
的奇偶性,并说明理由;
(2)若存在实数
使得
是奇函数,且在
上是严格增函数,请写出符合条件的两组
与
的值,并验证其符合题意;
(3)在(2)的条件下,求出所有符合题意的
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0a16226c3e25510313eafbb84e5c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca8b15a67c8c12cf9a7c9c4580c6736.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57da7d9f516da24dec5ae3b4998b3e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f404199c80633334c9027e09d2623f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0a16226c3e25510313eafbb84e5c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3b7a82459cef78caef0e9b55fbe470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(3)在(2)的条件下,求出所有符合题意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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