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问题 解答题

已知f（x）的定义域为（0，+∞），且满足f（4）=1，对任意x1，x2∈（0，+∞）都有f（x1?x2）=f（x1）+f（x2），当x∈（0，1）时，f（x）＜0。

（1）求f（1）；

（2）证明f（x）在（0，+∞）上是增函数；

（3）解不等式f（3x+1）+f（2x-6）≤3。

答案

解：（1）令，则f（1）=0；

（2）设，且，

则，

，

∴，

又当x∈（0，1）时，f（x）＜0，

∴，

∴f（x）在（0，+∞）上是增函数。

（3）令，则；

令，则，

∴，

可得，

解得：，

∴不等式的解集为(3，5]。

阅读理解

阅读理解

       This is a boy. His name is Tom. He has a nice cat. It is an English cat. It has black and gray hair. Lucy and Mike are Tom's friends. They have cats, too. Their names are Mimi and Maomao. They are Chinese

cats. They both have white hair. The English cat is five. The Chinese cats are three. They like their cats.

阅读短文，判断正(T)误(F)。

( ) 1. Lucy is Tom's friend.

( ) 2. Tom's cat is Chinese.

(     ) 3. The Chinese cats are five.

( ) 4. They like their cats.

( ) 5. Tom's cat is Mimi.
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阅读理解

阅读理解。

       1    !

     Wearing earphones, using complex Net language and constantly text messaging friends, the Gen-90s

following the Gen-80s begin to make their world debut (初次登台).

     Each generation or age group has its own symbols and lifestyle.   2       

     Earphones

     These little devices seem to grow on the heads of the Gen-90s. They might lead to MP3, MP4 or MP101

players, giving these young people a plugged-in, cool and perhaps self-addicted look, of course, life is not

always music to the ears.

     Martian language

     They have created their own code-like online language.   3  , so perhaps only Martians can understand.

This is an imaginative generation, though they need to be careful to keep it out of their term papers.

     Self-Portrait

     Saying "cheese" to their own digital cameras is usual for this generation. A little bit of narcissism (自恋)

never hurts anyone. It helps them reflect a little on their own lives.   4       

     Text-messaging 

       5  . This is a generation that respects efficiency. However, oral communication is important and will

never go out of style.

A. They take mobile phones with them everywhere.

B. Be aware of the risk of talking to strangers on line.

C. The Generation 90s is coming.

D. But be aware of the risks of posting private photos online.

E. Read on and judge for yourselves if you fit the Gen-90s group.

F. It's a mixture of English, Japanese and Chinese.

G. They can type their mobile phones as fast as they can speak.

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