选修4-5：不等式选讲已知函数f（x）=|x-a|．（1）若f（x）≤m的解_爱下问搜题

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问题解答题

选修4-5：不等式选讲

已知函数f（x）=|x-a|．

（1）若f（x）≤m的解集为{x|-1≤x≤5}，求实数a，m的值；

（2）当a=2且t≥0时，解关于x的不等式f（x）+t≥f（x+2）．

答案

（1）由于函数f（x）=|x-a|，由f（x）≤m可得-m≤x-a≤x+a，即a-m≤x≤a+m．

再由f（x）≤m的解集为{x|-1≤x≤5}，可得

a-m=-1

a+m=5

，解得

a=2

m=3

．

（2）当a=2时，f（x）=|x-2|，关于x的不等式f（x）+t≥f（x+2），即|x|-|x-2|≤t．

令h（t）=|x|-|x-2|=

2 ， x≥2

2x-2 ，0＜x＜2

-2 ， x≤0

，故函数h（x）的最大值为2，最小值为-2，不等式即 h（x）≤t．

①当t≥2时，不等式 h（x）≤t恒成立，故原不等式的解集为R．

②当 0≤t＜2时，（1）若x≤0，则h（x）=-2，h（x）≤t 恒成立，不等式的解集为{x|x≤0}．

（2）若 0＜x＜2，此时，h（x）=2x-2，不等式即 2x-2≤t，解得 x≤

t

2

+1，即此时不等式的解集为 {x|0＜x≤

t

2

+1 }．

综上可得，当t≥2时，不等式的解集为R； ②当 0≤t＜2时，不等式的解集为 {x|x≤

t

2

+1 }．

完形填空

       Brian is doing   1   now. He's working hard at school. He is happy in Canada.
       This week, he got to know   2   neighbourhood. On Monday, Jenny walked to school   3   him and
she showed him her favourite places. There   4   a bakery near his house. He can buy bread there.   5   his way to school, he can buy books at the   6  . He thinks   7   is not easy to live in a new neighbourhood.
Yesterday, he   8  . A young woman helped him   9   his way. Tomorrow, he   10

buy a map of the city.
He will keep it in his backpack. Then he won't get lost again.

( )1. A. good
( )2. A. he
( )3. A. with
( )4. A. has
( )5. A. At
( )6. A. shop
( )7. A. this
( )8. A. lost his way
( )9. A. finds
( )10. A. is going to

B. well
B. him
B. and
B. is
B. On
B. bakery
B. it
B. lost his street
B. find
B. goes to

C. happy
C. his
C. except
C. was
C. In
C. bookstore
C. what
C. lost his bag
C. found
C. went to

阅读理解

阅读理解。

Many people like animals, and often keep one or more of dogs and cats as pets(宠物). If you keep a dog or a cat

as a pet, you must look after it.

A grown-up(成年的)dog needs two meals a day-not more. It can eat meat, fish, rice and some other things. Dogs

like bones(骨头), but you can't give them chicken bones. Remember to give them a lot of clean water.

A dog should have a clean, dry box for sleeping(睡觉) in. Washing it once a week is good for its health. If it is ill,

take it to a vet(兽医). A healthy dog will bring you more pleasure.

Be careful when you choose(挑选)a cat. A cat has two meals a day with some meat or fish. It drinks a little milk

every day. Sometimes you can give them vegetables to eat. Don't forget that they need clean water to drink.

Take good care of your pets. They will be your good friends. Maybe they can give you some help when you are

in need.

Answer the questions.

1. What do dogs like eating?

__________________________________________________

2. Will pets be people's friends?

__________________________________________________

3.What kind of bones can't we give to the dogs?

__________________________________________________

4. What do cats like eating?

__________________________________________________

5. Why do we give cats and dogs two meals a day?

__________________________________________________