shuexue 集合

已知集合M={m＜x＜m+3/4}N={n-1/3＜x＜n}且MN都是集合{x|x大于等于0小于等于1}的子集,如果把叫做集合{x大于等于a小于等于b}的长度,那集合M交N长度的最小值为

(1):M: 0≤x≤0.75
N: 2/3≤x≤1
所以M交N={x|2/3≤x≤0.75}
所以长度=0.75-2/3=3/4-2/3=1/12
(2):设Y=(x+1)/(x-1)

则X=（y+1）/（y-1）

将X=（y+1）/（y-1）代入得

[（y+1）/（y-1）-1]f{[（y+1）/（y-1）+1]/[（y+1）/（y-1）-1]}+f[（y+1）/（y-1）]=（y+1）/（y-1）

[2/(y-1)]f{[2y/(y-1)]/[y/(y-1)]}+f[(y+1)/(y-1)]=(y+1)/(y-1)

两边同乘以y-1

2f{[2y/(y-1)]/[y/(y-1)]}+f[(y+1)/(y-1)]=(y+1)

2f{y}+f[(y+1)/(y-1)]=(y+1)

=2f{x}+f[(x+1)/(x-1)]=(x+1)

根据题目可得f[(x+1)/(x-1)]=[x-f（x）]/(x-1),代入上面得f(x)=1 （x不等于1）

（3）：