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问题 解答题
已知函数f（x）=
ax
x+1
（a为非零常数），定义：f1（x）=f（x），fk+1（x）=f[fk（x）]，k∈N*，例如：f2（x）=f[f（x）]，f3（x）=f[f2（x）]，…
（1）当a=2时，求f2(1)，f3(-
1
7
)的值；
（2）若对于任意x≠-1，等式f2（x）=x恒成立，求a的值；
（3）当a确定后，fk（x），k∈N*的值都由x的值确定．当a=2时，试通过对fk（x）的探究，写出一个使得集合{fk（x）}为有限集的真命题（不必证明）．
答案

（1）当a=2时，f（x）=

2x
x+1

∴f2（1）=f[f（1）]=f（1）=1

f3(-

1
7
)=f{f[f(-
1
7
)]} =f[f(-
1
3
)] =f(-1)无意义

（2）若对于任意x≠-1，等式f2（x）=x恒成立

∴f2（x）=

a•
ax
x+1
ax
x+1
+1
=
a2x
ax+x+1
=x恒成立即a2=（a+1）x+1恒成立

∴a=-1

（3）结合（1）满足条件的真命题为：函数f（x）=

2x
x+1
，若x=-
1
7
，则集合{fk（x）}为有限集．

阅读理解

阅读理解。

     Tom and Jim are brothers. They are from Australia. Tom is 14 years old and Jim is 13 years old. They speak English and French. Today they are in China. Now they are living in China. Their home is across from a park. There are five people in their family. They are their parents, their sister and them. Their mother is a teacher. Their father is a doctor. Their sister is very young. She doesn’t go to school. She goes to a kindergarten(幼儿园). They say China is a very interesting country. They like China.

1 Tom is from ______.

A. America        

B. Canada          

C. Australia          

D.UK

2. Tom and Jim speak ______.

A. Chinese and English            

B. English and French        

C. Chinese and Japanese              

D. French and Japanese

3. There are      __  people in Tom’s family

A. 3.        

B. 4.            

C. 5.                

D.6

4. Jim’s father is a ______.

A. doctor    

B. teacher        

C. writer            

D.farmer

5. Why do they like China?

A. Because they think Chinese food is nice.      

B. Because they like Chinese people.

C. Because they think China is an interesting country.      

D. We don’t know.
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单项选择题

若保险人未向投保人明确说明保险合同中的责任免除条款，将会导致( )的后果。

A．保险合同无效

B．该条款不产生效力

C．对该条款作不利于保险人的解释

D．可以减少投保人的保险费
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