问题 选择题
已知f(x)是定义在R上的偶函数,f(x)在[0,+∞)上是增函数,且f(
1
3
)=0,则不等式f(log
1
8
x
)>0的解集为(  )
A.(0,
1
2
)∪(2,+∞)
B.(
1
2
,1)∪(2,+∞)
C.(0,
1
2
D.(2,+∞)
答案

方法1:

因为函数f(x)是定义在R上的偶函数,

所以不等式f(log

1
8
x)>0等价为f(|log
1
8
x|)>0

因为函数f(x)在[0,+∞)上是增函数,且f(

1
3
)=0,

所以f(|log

1
8
x|)>f(
1
3
),即|log
1
8
x|>
1
3

log

1
8
x>
1
3
log
1
8
x<-
1
3

解得0<x<

1
2
或x>2.

方法2:已知f(x)是定义在R上的偶函数,f(x)在[0,+∞)上是增函数,且f(

1
3
)=0,

所以f(x)在(-∞,0]上是减函数,且f(-

1
3
)=0.

①若log

1
8
x>0,则log
1
8
x>
1
3
,此时解得0<x<
1
2

②若log

1
8
x<0,则log
1
8
x<-
1
3
,解得x>2.

综上不等式f(log

1
8
x)>0的解集为(0,
1
2
)∪(2,+∞).

故选A.

阅读理解

When you run, you put force that is equal to three times your body weight on your feet. The human foot contains twenty muscles. This means that there is a lot that can go wrong when you run.

Most sports have some kind of running or jumping So experts at many shoe companies work hard to design good sport shoes. First, a designer enters a plan for a shoe into a computer .Engineers then improve the design. A second computer designs a model for the shoe. Then a few pairs are made. Next, the shoe is tested.

Different kinds of sports shoes are made for different uses. Some are made to help marathon(马拉松) runners save energy during a race. Some are made for the stop-and-go kind of running tennis players. But all sport shoes have one thing in common: they are designed to help people’s feet comfortable during sports. Today, nearly every sport has its own special shoe designed for just the kind of running that sport needs.

小题1:The first in making a new shoe is to ________.

A.make a computer

B.put a design plan into a computer

C.design a shoe model

D.test several pairs小题2:Why are good sport shoes welcome to people?

A.Because they are comfortable to wear.

B.Because they help to develop leg muscles.

C.Because they help to change body weight.

D.Because they are both good and cheap.小题3:What is not talked about in the passage?

A.The number of the bones of human muscles.

B.The design for a shoe model.

C.The materials of sport shoes.

D.The effect of shoes upon sports.小题4:How many steps are there in the making of a shoe?

A.Three

B.Four

C.Five

D.Six小题5:Different kinds of sport shoes ________.

A.are made in different shoe companies

B.are designed for people of the different weight

C.are of the same price

D.meet the needs of different sportsmen

单项选择题