问题 解答题

已知函数f(x)=loga(3+2x),g(x)=loga(3-2x),(a>0,且a≠1).

(1)求函数f(x)-g(x)定义域;

(2)判断函数f(x)-g(x)的奇偶性,并予以证明;

(3)求使f(x)-g(x)>0的x的取值范围.

答案

(1)若使f(x)-g(x)的解析式有意义

须使f(x)=loga(3+2x),g(x)=loga(3-2x)的解析式都有意义

3+2x>0
3-2x>
   

 解得:-

3
2
<x<
3
2

所以函数f(x)-g(x)的定义域是(-

3
2
3
2

(2)函数f(x)-g(x)是奇函数,理由如下:

由(1)知函数f(x)-g(x)的定义域关于原点对称

又∵f(-x)-g(-x)=loga(3-2x)-loga(3+2x)

=-[loga(3+2x)-loga(3-2x)]=-[f(x)-g(x)]

∴函数f(x)-g(x)是奇函数

若f(x)-g(x)>0,即loga(3+2x)>loga(3-2x)

当a>1,则3+2x>3-2x,解得x>0,由(1)可得此时x的取值范围(0,

3
2

当0<a<1,则3+2x<3-2x,解得x<0,由(1)可得此时x的取值范围(-

3
2
,0)

阅读理解

阅读理解。

     Different people have different ideas about time. People in the USA think that it is important to

know the time. In cities in America, there are clocks in stations, factories and other buildings. Radio

announcers (播音员) give you the correct time during the day. Most Americans also have watches with

them wherever they go. They want to do certain things at certain time. They don’t like to be late.

     But time is not so important to everybody in the world. When you visit a country in South America,

you will find that people there don’t like to rush . If you had an appointment(约会) with somebody, he

could probably be late, because he may not want to arrive on time.

     In South America, even the radio programs may not begin on time. The men on the radio may not

think it is important to tell the exact time. People in South America think that clocks or watches are just

machines. They think that you let a clock or a watch control (控制) your life if you do everying on

time.

1.You can see clocks in stations, factories and other buildings in the USA because ___________.

A. Americans want to make these places beautiful

B. Americans want to sell these clocks

C. Americans think that it is important to know the time

D. Americans don’t think that it is important to know the time

2. Americans don’t want to be late when ______________.

A. they go to stations, factories or other buildings

B. they do certain things at certain time

C. they are free

D. their children go to school

3. The underlined word “rush” most probably means_____________.

A. jump  

B. hurry    

C. run    

D. have a watch

4. If you have an appointment with someone in South America, he may not arrive on time, and this is

because  _____________.

A. he doesn’t have a watch                

B. he forgets to have a watch with him

C. he doesn’t think it is necessary to arrive on time  

D. he doesn’t like to meet you

5. In this passage, we can see that time is very important to ______________.

A. people in the USA.                      

B. people in South America

C. everybody in the world.                  

D. children in school.

单项选择题