Last term,Peter was ____ at home.His parents were doing busines in another city. He felt lonely,so he often turned on the computer and played computer ____. However, sitting in front of the computer for a long time is ____ for him. And he spent little time on his study.He failed his exams.Luckily,his parents ____ his problem in time.They decided to come back home.Peter studies hard now.So far,he has made progress in his study.He ____ he can catch up with his classmates soon.

（1）已知函数f（x）=$\frac{x-7}{\left(a-1\right)x^2+4\sqrt{a-1}·x+5}$的定义域为R，求实数a的取值范围；

（2）不等式x﹣1＜2mx+3﹣m对于满足0≤m≤2的一切实数m都成立，求x的取值范围；

（3）设∫：A→B是从集合A到集合B的映射，在∫的作用下集合A中元素（x，y）与集合B元素（2x﹣1，4﹣y）对应，求与B中元素（0，1）对应的A中元素．

材料一：据估计，当时全国人口有2000万，秦始皇北筑长城征调三十万，南戍五岭又五十余万，修建阿房宫、骊山陵又七十余万，加上修驰道等其他徭役，每年征调服役的不下三百万。

材料二：公元前209年夏，有900多个农民被征发去渔阳戍守长城。他们走到大泽乡时，遇上大雨，道路泥泞，被迫停止前行，不能按期到达。按照秦法，戍守误期要被处死。他们当中的领队人……杀死了押队的军官……举起反抗的旗帜。

材料三：秦朝是由战国后期的秦国发展起来的中国历史上第一个大一统王朝，国祚共十五年。遥想当年“秦王扫六合”是何等的威风，可短短历经二世十几年即亡……