发布时间：2021-02-21 07:52:56
(本小题满分12分)已知二次函数对任意实数x都满足
，且．令.
（1）求的表达式；
（2）设，证明：对任意，恒有．
解：(1) 设
∴
∴
又 ∵，则
∴ ················································································ 5分
(2) ∵ 对
∴ 在[1，m]内单调递减
于是
······························· 8分
记，则
∴ 函数在是单调增函数
∴
∴ 命题成立··························································································· 12分
【解析】略