问题 解答题
已知全集U=R,A={x||x-1|≥1},B为函数f(x)=
2-
x+3
x+1
的定义域,C为g(x)=lg[(x-a-1)(2a-x)](a<1)的定义域;
(1)A∩B;CU(A∪B)
(2)若C⊆B,求实数a的取值范围.
答案

(1)解|x-1|≥1得:x≤0或x≥2∴A={x|x≤0,或x≥2};

∵函数f(x)的自变量x应满足2-

x+3
x+1
≥0,即
(x+1)(x-1)≥0
x+1≠0

∴x<-1或x≥1∴B={x|x<-1,或x≥1};

A∩B={x|x<-1,或x≥2},

A∪B={x|x≤0,或x≥1},

CU(A∪B)={x|0<x<1}

(2)∵函数g(x)的自变量x应满足不等式(x-a-1)(2a-x)>0.

又由a<1,∴2a<x<a+1∴C={x|2a<x<a+1}

∵C⊆B∴a+1≤-1或2a≥1∴a≤-2或a≥

1
2

又a<1∴a的取值范围为a≤-2或

1
2
≤a<1.

阅读理解

阅读短文, 根据要求完成下面各小题。

Canada is one of the best places in the world for a skiing(滑雪) vacation. Here are some good resorts(胜地) for skiing in Canada.

Canmore, one of the best resorts, is in Alberta, Canada. It is cheap and you can also stay in the National Park.

Another great place is Marmot Basin. This beautiful ski resort is also in Alberta. It’s one of the least crowded ski resorts in North America. 71. You can spend more time on the slopes(斜坡) and don’t need to wait to go back up the mountain.

Mount Tremblant Resort is in the beautiful Laurentian Mountains. It has a beautiful village(乡村), with a lot to see and do. This is a great place to enjoy winter and skiing.

Kicking Horse Mountain Resort is a four-season(季节) mountain resort. It is in the Canadian Rockies. You can enjoy skiing and sightseeing during the day and relax in the quiet hotel during the evening.

Have a look at these places before planning your skiing vacation. You are sure to find one you like.

(一)根据短文内容,回答下列各题。

小题1:How many places for skiing in Canada are mentioned(提到) in this passage?

_________________________________________________________________

小题2:Which two ski resorts are in Alberta?

_________________________________________________________________

(二)将文中划线的句子译成汉语。

小题3:_____________________________________________________________

(三)给短文拟一个合适的标题。

小题4:_____________________________________________________________

单项选择题