题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-33145.png)
(1)若直线y=kx+1与f(x)的反函数图象相切,求实数k的值;
(2)设x﹥0,讨论曲线y=f(x)与曲线y=mx2(m﹥0)公共点的个数;
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-66944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-22153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-97061.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-88167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-11219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-89053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-76489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-22153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-80965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-97061.png)
解析
试题分析:(1)f (x)的反函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-12668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-92663.png)
(2)曲线y=f(x)与曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-54003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-14986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-86948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-77326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-77326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-22313.png)
(3) 比较两个式子的大小的一般方法是用比较法,即作差,变形,判断符号.
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-88309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-43385.png)
结合这个式子的特征可看出,我们可研究函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-64633.png)
试题解析:(1)f(x)的反函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-12668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-12668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-92663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-84822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-88167.png)
(2)当x>0,m>0时,曲线y=f(x)与曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-54003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143819-14986.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-51709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-54512.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-33138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-62053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-85957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-33138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-39904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-85957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-23006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143821-33138.png)
所以对曲线y=f(x)与曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-54003.png)
当m
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-11219.png)
当m=
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-89053.png)
当m
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-76489.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-40627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-75504.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143820-64633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-73444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-87188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-98649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143822-87188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-40389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-99341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-95711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-28556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-40389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-10561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143823-40389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143824-84764.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143824-95046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143824-81527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-66944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143824-87433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143825-87710.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-66944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143816-22153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143818-80965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143817-97061.png)
核心考点
试题【己知函数f(x)=ex,xR.(1)若直线y=kx+1与f(x)的反函数图象相切,求实数k的值;(2)设x﹥0,讨论曲线y=f(x)与曲线y=mx2(m﹥0)公】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143807-16735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143807-97616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143808-23468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143808-29612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143808-23468.png)
A.-3![]() ![]() | B.-3![]() ![]() |
C.-3![]() ![]() | D.-3![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143744-92187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143744-92521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143745-17002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143745-16903.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143735-15977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143735-65385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143735-77961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143735-83617.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143725-43791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143725-50656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143725-15015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143725-16521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143725-20453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143726-11909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143726-84749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143726-11909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143726-14217.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143615-87192.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-67974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-52563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-47727.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-59252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-61956.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143616-67974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143617-67962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143617-82620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204143617-42020.png)
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