[f<x1>-f<x2>]/[x1-x2] <0,
即是曲線上任意兩點連線的斜率k<0
那么函數(shù)為減函數(shù)
∵函數(shù)y=f<x-1>的圖像關(guān)于點(1,0)對稱
f(x)圖像向右平移2個單位得到f(x-1)圖像
∴f(x)圖像關(guān)于(0,0)對稱
即f(x)是奇函數(shù)
對任意的x,y∈R,不等式f(x^2-2x)+f(2y-y^2)≤0成立
即f(x^2-2x)≤-f(2y-y^2)=f(y^2-2y)
∴x^2-2x≥y^2-2y
∴x^2-y^2-2x+2y≥0
(x-y)(x+y)-2(x-y)≥0
(x-y)(x+y-2)≥0
又1≤x≤4
構(gòu)成的區(qū)域如圖:
y/x的范圍[-1//2,1]
![](http://h.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=c484a91dd462853592b5da27a0df5afe/0b46f21fbe096b63a9f08dbf0d338744eaf8ac70.jpg)