题干

设a>1,函数f(x)的图象与函数y=4﹣a|x﹣2|﹣2•ax﹣2的图象关于点A(1,2)对称.

(1)求函数f(x)的解析式;

(2)若关于x的方程f(x)=m有两个不同的正数解,求实数m的取值范围.

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答案(点此获取答案解析)

解:(1)设点P(x,y)是函数f(x)图象上任意一点,P关于点A对称的点为P′(x′,y′),则
x
+
x
'
2
=1

同类题1

阅读下面短文,从所给的四个选项(A、B、C和D)中,选出可以填入空白处的最佳选项。

    Once, a professor held a test on his students. The professor started with the following question, “Now,1 you are going to cut trees on a hill. One of the trees has a big 2 while the other's small. Which will you cut?” The question got a quick 3, “Of course the big one! No need to4 .”

    The professor5, “The big tree is a poplar(白杨)6seen everywhere, while the small one is a Korean pine. Consider again?” A second7brought students more sense: a Korean pine is much more8than the poplar, so they changed their decision. “9 we'll cut the pine. The poplar isn't worth our10.”  Smile still11on the professor's face. “But the pine's trunk is less12than the poplar.” Rather puzzled, they became13, then said, “While, we'll cut the poplar.” The professor gave more detail. “14the poplar is straight, the trunk became empty within. Then what's your choice?”

    Finally one of the students lost his15and said, “Professor, you have asked a series of questions leading us to change our answers16. What do you want to 17 after all?”

    The professor's smile18. He said, “Why none of you ask me for what purpose to cut the tree? Though my questions 19all the way, they are decided by one thing: your20to take the action. If it aims at making handicraft articles you may cut the pine; if you just want to have some firewood, you'd better cut the poplar.”

同类题2

阅读下面的文章,完成后面小题

最美的姿态

       ①阅读与不阅读,显示出两种截然不同的生活方式或人生方式。一面草长莺飞,繁花似锦,一面必定是一望无际、令人窒息的荒凉和寂寥。

       ②一种人认为:人既然作为人,存在着就必须阅读。肉体的滋长、强壮与满足只需五谷与酒肉,但五谷与酒肉所饲养的只是一具没有灵魂、可以行走、可以叫嚣的躯体。人应该是一种追求精神并从精神上获得愉悦的动物,这种动物是需要通过修炼的,而修炼的重要方式之一便是阅读。

       ③另一种人,即使书籍堆成山耸立在他们面前,他们也不可能思考一下这些书与他们自己的人生或生活有何关系。吸引这些人的只是物质与金钱,再有便是各种各样的“娱乐”。

       ④人这一辈子,无论怎样辛劳、勤勉,实际上只能在极小的范围内经历生活,经历人生。由于如此,人认知世界,十有八九是盲人摸象,很难有对世界的完整把握,而图书呈现了人类在不同时期、不同领域的不同经验。一个识字人,只需有书在手,坐在家中,或案前,或榻上,或瓜棚豆架之下,便可走出生活圈栏,进入一个无边的疆域。明明是身居斗室,却从别人的文字里看到了沙漠驼影、雪山马迹、深宫秘事、坊间趣闻……读书渐久,经验渐丰,你会发现,读书使人的心灵宛如雨后的池塘,逐渐充盈。

       ⑤读书人的高贵气质是由连绵不断的阅读潜移默化养就的。有些人,就造物主创造的毛坯而言,也许是没有魅力的,甚至是有缺陷不完美的。然而,读书生涯使他们由内到外获得了新生。虽然还是从前的身材与面孔,却有了一种比身材、面孔高贵得多的叫“气质”的东西。一些以读书为生的先生,当他们安坐在藤椅里向你平易近人地叙事或论理,当他们站在讲台上条分缕析地讲述他们的发现,当他们在餐桌上很随意地诙谐了一下时,你会觉得这些先生真是很有神采。此时,你就会真正领略“书卷气”的迷人之处。

       ⑥人类无疑是一切动物中最善于展示自身的动物,体育场、舞台、T型台……这一切场所,都是人类展示自己身体以及姿态的地方,但你知道吗?人类最优美的姿态是读书。

                                                                                                                                                                   (选自《北大中文系第一课》,有删改)