问题 选择题

已知f(x)是定义在R上的增函数,函数y=f(x-1)的图象关于点(1,0)对称.若对任意的x,y∈R,不等式f(x2-6x+21)+f(y2-8y)<0恒成立,则当x>3时,x2+y2的取值范围是(  )

A.(3,7)

B.(9,25)

C.(13,49)

D.(9,49)

答案

∵函数y=f(x-1)的图象关于点(1,0)对称

∴函数y=f(x)的图象关于点(0,0)对称,即函数y=f(x)为奇函数,则f(-x)=-f(x)

又∵f(x)是定义在R上的增函数且f(x2-6x+21)+f(y2-8y)<0恒成立

∴(x2-6x+21)<-f(y2-8y)=f(8y-y2 )恒成立

∴x2-6x+21<8y-y2

∴(x-3)2+(y-4)2<4恒成立

设M (x,y),则当x>3时,M表示以(3,4)为圆心2为半径的右半圆内的任意一点,

则x2+y2表示在半圆内任取一点与原点的距离的平方

结合圆的知识可知13<x2+y2<49

故选 C

阅读理解

阅读理解。

     About twenty of us had been fortunate enough to receive invitations to a film-studio (影棚) to take

part in a crowd-scene. Although our "act" would last only for a short time, we could see quite a number

of interesting things.

     We all stood at the far end of the studio as workmen prepared the scene, setting up trees at the edge

of a winding path. Very soon, bright lights were turned on and the big movie-camera was wheeled into

position. The director shouted something to the camera operator and then went to speak to the two

famous actors nearby. Since it was hot in the studio, it came as a surprise to us to see one of the actors

put on a heavy overcoat and start walking along the path. A big fan began blowing tiny white feathers

down on him, and soon the trees were covered in "snow". Two more fans were turned on, and a "strong

wind" blew through the trees. The picture looked so real that it made us feel cold.

     The next scene was a complete contrast (对比). The way it was filmed was quite unusual. Pictures

taken on an island in the Pacific were shown on a glass screen (幕). An actor and actress stood in front

of the scene so that they looked as if they were at the water's edge on an island. By a simple trick like

this, palm trees, sandy beaches, and blue, clear skies had been brought into the studio!

     Since it was our turn next, we were left wondering what scene would be prepared for us. For a full

three minutes in our lives we would be experiencing the excitement of being film "stars"!

1. Who is the author?

A. A cameraman.

B. .A film director.

C. A crowd-scene actor.

D. A workman for scene setting.

2. What made the author feel cold?

A. The heavy snowfall.

B. The man-made scene.

C. The low temperature.

D. The film being shown.

3. What would happen in the "three minutes" mentioned in the last paragraph?

A. A new scene would be filmed.

B. More stars would act in the film.

C. The author would leave the studio.

D. The next scene would be prepared.

单项选择题