解题方法
1 . 已知幂函数
为偶函数.
(1)求幂函数
的解析式,判断
在
上的单调性,并用定义证明;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02299c5436edc085abf0bc2b8f3959fd.png)
(1)求幂函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8df28b10595f7c22030ab2a2cf9640.png)
您最近一年使用:0次
解题方法
2 . 已知
是幂函数,且在
上单调递增.
(1)求
的值;
(2)若函数
,证明:
的值是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413615915fe22bbaf38f3d9ca695c753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357ad3c8994f634bd88d7ae09f4cd089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d279d6aa3b05d504caa45c7e0208284.png)
您最近一年使用:0次
3 . 已知幂函数
,且
在区间
上单调递减.
(1)求
的解析式及定义域;
(2)设函数
,利用单调性定义证明:
在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdf2ba01cf7e2f6c15cc87262432b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26806a3a37309470b7d729844a9e2d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
名校
4 . 已知点
在幂函数
的图象上
(1)求
,
的值;
(2)证明:函数
在
是增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f639b41a2fe03c022a8cc26255d112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb364ac31994e88f92f584d9702cea1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26806a3a37309470b7d729844a9e2d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
5 . 已知幂函数
(
)的定义域为
,且在
上单调递增.
(1)求m的值,并利用单调性的定义证明:函数
在区间
上单调递增.
(2)若存在实数
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abac545d0f729c6294056d6984cf47d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef58f901e8893e186ad1f64822121be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(1)求m的值,并利用单调性的定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1faa69ee32f72a475e7dbb8d9bc58ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9285ab9f42e86dfee0952590d2de7a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
6 . 幂函数
是偶函数,
(1)求
的值,写出
解析式;
(2)
,
①判断
的奇偶性,并用定义证明;
②指出
的单调递减区间(无需证明),并解关于实数
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4126828d35bbf316e044e22fe24d4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40556aaf289536183c29057e437a1b69.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
②指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14d251fc38c2f3e8231c3e5c4eea6dc.png)
您最近一年使用:0次