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问题 解答题
仔细阅读下面问题的解法：
设A=[0，1]，若不等式21-x-a＞0在A上有解，求实数a的取值范围．
由已知可得  a＜21-x
令f（x）=21-x，不等式a＜21-x在A上有解，
∴a＜f（x）在A上的最大值
又f（x）在[0，1]上单调递减，f（x）max=f（0）=2
∴a＜2即为所求．
学习以上问题的解法，解决下面的问题：
（1）已知函数f（x）=x2+2x+3 （-2≤x≤-1）求f（x）的反函数及反函数的定义域A；
（2）对于（1）中的A，设g（x）=
10-x
10+x
x∈A，试判断g（x）的单调性；（不证）
（3）又若B={x|
10-x
10+x
＞2x+a-5}，若A∩B≠Φ，求实数a的取值范围．
答案

（1）f（x）=（x+1）2+2

∵f（x）在[-2，-1]上单调递减

∴f（x）∈[2，3]

故反函数的定义域A=[2，3]（2分）

令x+1=-

y-2
，x=-1-
y-2

∴f-1（x）=-1-

x-2
  x∈[2，3]（4分）

（2）g（x）=

10-x
10+x
=-1+
20
10+x
  x∈[2，3]

g（x）在x∈[2，3]上单调递减           （8分）

（3）由A∩B≠Φ，⇒不等式

10-x
10+x
＞2x+a-5在集合A上有解，

亦即不等式a＜

10-x
10+x
-2x+5在集合A上有解，（10分）

令函数h（x）=

10-x
10+x
-2x+5，

a＜h（x）在集合A上有解，⇒a＜h（x）在集合A上的最大值

又h（x）=-1+

20
10+x
-2x+5=
20
10+x
-2x+4 在区间A上单调递减

h（x）max=g（2）=

5
3
⇒a＜
5
3

⇒实数a的取值范围为（-∞，

5
3
）                               （12分）

阅读理解

An 18-year-old student has won a local election to become mayor of his hometown in the US state of Michigan. Michael Sessions won by the slenderest of margins - just two votes put him ahead of his only rival, the incumbent 51-year-old mayor. Mr. Sessions attributed his electoral success to the votes cast by his parents. He will now have to juggle schedules between attending school and fulfilling his civic duties. He will attend his school classes between 8am to 3pm and carry out his new job as the elected mayor of Hillsdale before dinner at 6pm. He aims to deliver on his campaign pledges of increasing the contingent (小分队) of full-time fire-fighters from three to four, revitalizing (使恢复元气) the local economy and enabling townsfolk to air their views and grievances on town life.

Mr. Sessions was too young to enter the election when it was first announced – he turned 18 only in September, which meant he had just four weeks of campaigning. Although he is the youngest elected official in America, he cannot celebrate his success with champagne because he would be arrested for underage drinking. He ran for office with a budget of $700, which he made from his summer job of selling toffee apples. His position is largely ceremonial and he will not get his own office. Instead, he will receive an annual stipend of $3,600 to cover basic expenses. He starts his four-year position on November 21. Mr. Sessions has become an overnight celebrity since his victory and has already done the circuit of television chat show interviews.

1. When did the election probably take place?

A. August.        B. September.         C. October.       D. December.

2. How long will Mr. Sessions be the mayor of Michigan State?

A. One year.           B. Two years.         C. Four years.     D. Not mentioned.

3. Which of the following statements is correct?

A. Mr. Sessions won the election by two votes.

B. Mr. Sessions had many competitors during the election.

C. The new mayor will get an office after the election.

D. The new mayor doesn’t have to attend the school any more.
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判断题

系统运行数据中涉及基金投资人信息和交易记录的备份应当在不可修改的介质上保存10年。()
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