问题 解答题
已知奇函数函数f(x)的定义域为(-∞,0)∪(0,+∞),当x>0时,f(x)=1-
1
x

(1)求f(-2)的值;
(2)当x<0时,求f(x)的解析式;
(3)求证:函数f(x)在区间(0,+∞)上是单调增函数.
答案

(1)∵函数f(x)为奇函数,定义域为(-∞,0)∪(0,+∞),

x>0时,f(x)=1-

1
x

f(-2)=-f(2)=-

1
2
…(4分)

(2)设x<0,则-x>0,

f(-x)=1-

1
-x
=1+
1
x
…(6分)

∵函数f(x)为奇函数

∴当x<0时,f(x)=-f(-x)=-1-

1
x
…(9分)

(3)证明:任意0<x1<x2

f(x1)-f(x2)=-

1
x1
+1-(-
1
x2
+1)

=

1
x2
-
1
x1
=
x1-x2
x1x2

∵0<x1<x2,∴x1-x2<0,x1x2>0,

x1-x2
x1x2
<0,即f(x1)<f(x2),

故f(x)在(0,+∞)上为增函数.

阅读理解
阅读理解。
下面两封是Celia写给她的老师Mr. Scott的信以及Mr. Scott给她的回信。
Dear Mr. Scott,
     I'm writing to complain about my deskmate, Lana. She likes junk food (垃圾食品) and she always
brings some to school. After she eats it, she drops the litter into my desk. She also has a bad habit. After
she borrows my pencil, she doesn't return it. I get angry when she copies (抄袭) my homework. And she sometimes makes ink marks (墨迹) on my clothes with her pen. These things always happen and she
doesn't care about my feelings. I need your help. Can you let me have another deskmate?
                                                                                                                                       Celia
Dear Celia,
     I'm sorry to hear that Lana has so many bad habits. And I'm glad that you discuss your problems
with me.
     I talked to Lana yesterday. She said she did these things because of her carelessness(粗心). She
wanted to be polite with our help. She agreed to put the litter in a bag. She said she would do her own
homework and be careful with her pen. She asked you to remind (提醒) her by saying "Would you mind
returning my pencil?"    
     Would you mind not changing your deskmate? She is a nice girl. It's important for you to help each
other and you will understand each other better.
                                                                                                                                            Scott
Celia's problems with LanaLana's solutions (解决方法)
She drops the litter into my desk.1. ________________________
2. ________________________You can remind me by saying "Would you mind
returning my pencil?"
3. ________________________4.________________________
5.________________________I will be careful with my pen.
多项选择题