题目
题型:解答题难度:一般来源:不详
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-80728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-25399.gif)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-54175.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-50621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-92426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-36380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-73929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-34238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-77864.gif)
答案
(1)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-18033.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-64061.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-81470.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-57724.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-80728.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-84905.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-76903.gif)
(1)当a=0时h(x)="-x+1,"
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-98477.gif)
所以 当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-15139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-69943.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060921-98477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060922-14165.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060922-55241.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060922-74247.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060922-95436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060922-88297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-23287.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-64061.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-22144.gif)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-66815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-78013.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-93049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-91756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-58742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-18448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-45932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-14443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-59069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060925-38358.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-58742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-18448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060925-40823.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060925-32999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-91756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-58742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-18448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060925-62596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-14443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060924-59069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
综上所述:
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-18033.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-64061.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-81470.gif)
函数f(x)在(1,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-99395.gif)
(Ⅱ)因为a=
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060925-18688.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-41032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-61992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-72749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060923-91756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-22502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-19716.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060926-57654.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-89406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-18193.gif)
由于“对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-36380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-73929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060919-34238.gif)
“
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-62794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-59350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060918-55701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-22359.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060927-62794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060928-18035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060928-33598.gif)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060928-17796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060928-96332.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060928-46886.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060929-29940.gif)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060929-63148.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060929-24899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060929-22989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060929-54904.gif)
综上,b的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060920-57724.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060916-85190.gif)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060912-30303.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060912-10727.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060913-68003.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060913-44015.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060913-61050.gif)
(2)若关于
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060913-65818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060913-53899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060914-34286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060914-29704.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060903-65024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060903-40443.gif)
(Ⅰ)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060903-52524.gif)
(Ⅱ)试判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060903-90988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060903-78974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060904-46018.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060904-14482.gif)
(Ⅲ)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060904-85785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060904-18045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060904-97265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060905-38707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060859-22699.gif)
A.a≥3 | B.a≤-3 | C.a<5 | D.a≥-3 |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818060857-30878.gif)
A.![]() | B.![]() ![]() | C.![]() | D.![]() |
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