题目

已知函数是定义在上的奇函数，且， （1）确定函数的解析式； （2）用定义证明在上是增函数； （3）解关于的不等式． 答案：（1）（2）证明见解析（3） 【解析】 （1）利用奇函数的性质，结合列方程组，解方程组求得的值，也即求得函数的解析式. （2）任取，通过计算，证得函数在上是增函数. （3）利用奇函数的性质化简不等式，在根据函数的定义域和单调性列不等式，解不等式求得的取值范围. 【详解】解：（1）依题意How often one hears children wishing they were grown-ups and old people wishing they were young again. Each age has its pleasures and its pains, and the happiest person is the one who enjoys what each age gives him without wasting his time in useless regrets.   　 Childhood is a time when there are few responsibilities to make life difficult. If a child has good parents, he is fed, looked after and loved, whatever he may do. It is impossible that he will ever again in his life be given so much without having to do anything in return. What's more, life is always presenting new things to the child — things that have lost their interest for older people because they are too well-known. But a child has his parents. He is not so free to do what he wishes to do; he is continually being told not to do things or being punished for what he has done wrong. 　 When the young man starts to earn his own living, he can no longer expect others to pay for his food, his clothes, and his room, but has to work if he wants to live comfortably. If he spends most of his time playing about in the way that he used to as a child, he will go hungry. And if he breaks the laws of society as he used to break the laws of his parents, he may go to prison. If, however, he works hard, keeps out of trouble and has good health, he can have the great happiness of building up for himself his own position in society. 1. According to the second paragraph, the writer thinks that __. 　　A. life for a child is comparatively easy 　　B. a child is always loved whatever he does 　　C. if much is given to a child, he must do something in return 　　D. only children are interested in life 2. After a child grows up, he __. 　　A. will have little time playing　　　 B. has to be successful in finding a job 　　C. can still ask for help in time of trouble D. should be able to take care of himself 3. Which of the following statements is NOT true according to the passage? 　　A. People are always satisfied with each part of their life. 　　B. Life is less interesting for old people. 　　C. Adults(成年人) are free to do what they want to do. 　 D. Adults should no longer rely on（依赖）others. 4. The underlined word “responsibilities” in the second paragraph means_________. 　　A. duties  　　B. jobs   　　C. suggestions 　　D. desires 5. The main idea of the passage is _________ . 　　A. life is not enjoyable since each age has some pains 　　B. young men can have the greatest happiness if they work hard 　 C. childhood is the most enjoyable time in one's life 　 D. one is the happiest if he can make good use of each age in his life.