解题方法
1 . (1)解不等式:
.
(2)已知
都是正数,求证::
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03f5e2ce625506cc6901e3bbfd57616.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca946693693753e4b53403dfff80761.png)
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解题方法
2 . 已知
是定义在R上的奇函数,且
时有
.
(1)写出函数
的单调区间(不要证明);
(2)求函数
的解析式;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5749bb82edfb623c63ae4ec6b4d43da8.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369100ccd44feaa77e5f119ea949a879.png)
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3 . (1)解不等式:
;
(2)已知
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3b76cedebe03e7ba487b2989e91440.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d89ab55ffb93cc48f077b542dbd25aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45a429bc958c8a31096ead597b97501.png)
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解题方法
4 . 已知函数
.
(1)证明:函数
是奇函数;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2802c53543e37ee05126bb01c09895f7.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e136393c53d7926c26083ba8c9c3c6.png)
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5 . 利用十字相乘法分解因式:
(1)
;
(2)
.
(3)求方程
的解集.
(4)求证:对任意的x,a,b,都有
.
(5)已知“任意l和s,都有
”是真命题,借助这个结论将
进行因式分解.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdf57778bfe4dab4ee539f27ec9758c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96791c33798bd64168fbcfed8227e3d7.png)
(3)求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86eb4ca4061cc0763ceb703feebc2b69.png)
(4)求证:对任意的x,a,b,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22f618009ca40d3c793a14fdbf1b32d.png)
(5)已知“任意l和s,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84b242ba1b490d6179e5f68f425bcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ac4ca64fdb94ebfac63b6d45a453be.png)
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2023高一·全国·专题练习
名校
解题方法
6 . 已知函数
,
(
).
(1)当
时,解关于x的不等式
;
(2)判断函数
的奇偶性,并证明;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6987701d00f14d9c9cd45cbdb000607b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597ca5bf7e8d0959c1ca65962b6a4200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49341b57eb107f416a014903ce25a8.png)
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解题方法
7 . 已知集合
.
(1)求证:
的充要条件是
;
(2)若
是
的充分不必要条件,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ea30f17181e16a52da2925d19b512d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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8 . 设函数
.
(1)当
时,求函数
的解集;
(2)是否存在实数
,使得任意
,都有
恒成立,若存在,请求出求实数
的取值范围,若不存在,请证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc064736a1befa135f1633a1a72693b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . (1)已知
,
,
,求证:
;
(2)当
时,不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2129e8ec4f374ae282fb9785461a64c7.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d30ce13f0555c28c8bfc435b1a640a8.png)
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2023高一·全国·专题练习
名校
解题方法
10 . 在集合论中“差集”的定义是:
,且
(1)若
,
,求
;
(2)若
,
,求
;
(3)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f4bcaec7926363d8f77c6e773920d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b998f1e3675e0fa3b790c416a751af63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e6ad1166c7625e63b80e75b2fb1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2755a85584173902f146eacf40102723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cb7961d2d6957cfd6b4af403450e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7321a9fa7a6ef6be6e40c96709763930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6846ad147da3f53658602eade09631d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe3404ade72e644b48d19572c173c93.png)
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