题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-37200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-35130.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-36780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-27551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-78531.gif)
(1)求证:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-37200.gif)
(2)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010548-37200.gif)
(3)求不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-80681.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-21456.gif)
令x=y=-1, 得f(1)= f(-1
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-84132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-21456.gif)
再令y=-1, 得f(-x)= f(x)+ f(-1)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-21456.gif)
(2)在①中令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010549-95602.gif)
先讨论
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010550-75136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010550-40250.gif)
由③知:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010550-82983.gif)
∵偶函数图象关于y轴对称 ,∴f(x)在(-∞,0)上是减函数;
(3)∵f[x(x-3)]= f(x)+ f(x-3)≤2, 由①②得2=1+1= f(2)+ f(2)= f(
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010550-77045.gif)
1)若x(x-3)>0 , ∵f(x)在(0,+∞)上为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010550-69138.gif)
由f[x(x-3)] ≤f(4) 得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010551-71294.gif)
2)若x(x-3)<0
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010551-89086.gif)
由f[x(x-3)] ≤f(-4)得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010551-37171.gif)
∴原不等式的解集为:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010551-93158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010551-68178.gif)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010547-38482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010547-74137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-47444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-57934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-88290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-88091.gif)
有:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-76825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-13800.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-88141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-50582.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-75517.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-47444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010541-75449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010542-99597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010542-93910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010540-47444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010542-45009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010542-53180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010536-72438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010536-58034.gif)
(1)求实数c的值;
(2)解不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010536-90862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010524-98790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010525-66601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010525-11936.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010525-36237.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010525-39059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010525-27284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010524-98790.gif)
⑴ 任取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-80596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-73623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-51633.gif)
⑵ 对于
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010524-98790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-20730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-59005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-84347.gif)
我们将满足上述两条件的函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-50571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010526-51633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-14432.gif)
(1)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-11050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-43091.gif)
(2) 已知
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010528-70147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010528-23790.gif)
(3)对于(2)中的函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010527-50571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010528-65132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010528-27164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010528-63494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010523-77510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818010524-31803.gif)
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