问题 解答题

已知函数f(x)=loga(x+1)(a>1),若函数yg(x)的图象上任意一点P关于原点对称的点Q的轨迹恰好是函数f(x)的图象.

(1)写出函数g(x)的解析式;

(2)当x∈[0,1)时总有f(x)+g(x)≥m成立,求m的取值范围.

答案

(1)y=-loga(1-x)(x<1)(2)(-∞,0]

(1)设P(xy)为g(x)图象上任意一点,则Q(-x,-y)是点P关于原点的对称点,因为Q(-x,-y)在f(x)的图象上,所以-y=loga(-x+1),

y=-loga(1-x)(x<1).

(2)f(x)+g(x)≥m

即logam.

F(x)=logax∈[0,1).

由题意知,只要F(x)min≥m即可.

因为F(x)在[0,1)上是增函数,所以F(x)min=F(0)=0.

m的取值范围是(-∞,0].

阅读理解

阅读理解。

  He is quiet and shy. He likes to hide his eyes behind his hair. He doesn't

smile very often. However,  if you talk to him about music, he'll have a lot to say.                  This is Jay Chou, the 24-year-old Taiwanese pop king(天王). His fans are

so excited because he will sing songs in Beijing on September 12. Those songs

are from his new album (唱片), "Ye Huimei", and the album was released

(发行) in July and was named after his mother.

  Chou grew up just with his mother. He did not talk much and did badly in

many school subjects.

  His mother noticed the boy's special interest in music and sent him to learn

piano when he was only three years old. He loved it and kept on practicing.

  Chou is not very handsome. He does not speak clearly when he sings or

talks. But the singer has huge crowds of fans. "He is really good at music. It

makes him attractive(有魅力的) to me, " said Liu Jiajun,  a Junior 2 student in

No. 101 Middle School in Beijing.

  "He is true to himself. He never follows others, "said Zhang Yujie, a Junior

1 girl at Huaibei Middle School in Sihong, Jiangsu Provice.

1. From this passage, we know that Jay Chou _____.

A. is very handsome            

B. has a bright smile

C. often makes too much noise    

D. is a pop music star

2. His fans are so excited because _____.

A. he released a new album in July  

B. he will sing new songs in Beijing

C. he can play the piano very well

D. his new album was named after his mother

3. When he was a little child, he _____.

A. talked a lot every day    

B. did well in his study at school

C. started to like music      

D. had huge crowds of fans

4. According to one of his fans, Jay _____.

A. is a good student        

B. has long and beautiful hair

C. is a well-known pianist    

D. is very attractive to them

5. The sentence "He never follows others" in the last paragraph means _____.

A. he always has his own style            

B. he likes to walk alone

C. he doesn't like other people's songs at all  

D. no one can catch up with him

单项选择题