名校
解题方法
1 . (1)解关于x的不等式
;
(2)求函数
的定义域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95dc69810bcd61c0032ff275e9cc53ba.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b2fee56c519b69e148925975317a28.png)
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名校
解题方法
2 . 已知函数
(
且
)为奇函数.
(1)求实数
的值;
(2)若
,求函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8788e0cbf25b5b7ab437952fc1e7315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30e01790ac61851c453cbef2d5245d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
3 . 试讨论函数
的定义域、值域、单调性,并画出图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519192532883d560482ad071e7b54c4.png)
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24-25高一上·全国·课后作业
解题方法
4 . 设
,且
,求下列函数的定义域:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1f6f73cfb1438fca4e6957abbace1e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bfe784d9f5f0333ec3942e1e4bb184.png)
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5 . 已知函数
.
(1)若
的定义域为
,求
的定义域;
(2)证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b879f93babf292763dd1ee52f4d2c4d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5872abdb3911443a2090f0e95e442447.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48824632c5ca0107f0ca4fc4bd12de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4efc8f466b7f221d919f927dde5141.png)
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6 . 设函数
.
(1)求
的定义域;
(2)求
的单调区间;
(3)求
在区间
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de676d0ea60cf177f85d7d8eedb4f59e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc7bc07dde43da45e75bb38793257f0.png)
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7 . 已知函数
.
(1)求函数的定义域;
(2)求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b759362f728c996b0ec55ad730e956.png)
(1)求函数的定义域;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff1ca955e03dc13e97f8efb848edcdf.png)
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8 . 已知函数
的定义域为集合
,集合
.
(1)若
,求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759336bc4a1d02713f41320503423d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbcb06cf20c2e87fd69513c117936f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170ed92b09d13465657b81d1defedec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
的定义域,并判断其奇偶性;
(2)判断函数
在
上的单调性,并用单调性的定义加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
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10 . 已知函数
的定义域是
,若对于任意
,都有
,且
时,有
.令
.
(1)求
的定义域;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63cb59d5f3eb16beb379672fde5f170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee3a00fbaf95e5647c79000f4c2eae5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
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