问题 填空题
已知定义在R上的函数f(x),满足f(x)=-f(x+
3
2
),f(-1)=1,f(0)=-2
,且y=f(x-
3
4
)
是奇函数,则f(1)+f(2)+…+f(2009)=______.
答案

f(x)=-f(x+

3
2
)⇒f(x+3)=f(x)⇒f(2)=f(-1)=1,f(3)=f(0)=-2

又∵y=f(x-

3
4
)是奇函数

⇔f(-x-

3
4
)=-f(x-
3
4
)⇔f(-x)=-f(x-
3
2
)

f(

1
2
)=-f(-2)=-f(1),

f(

1
2
)=-f(2)=-1,

∴f(1)=1

∴f(1)+f(2)+…+f(2009)=

f(1)+f(2)=2.

故答案为:2

单项选择题
单项选择题

Our ape-men forefathers had no obvious natural weapons in the struggle for (1) in the open. They had neither the powerful teeth nor the p claws of the big cats. They could not (2) with the bear, whose strength, speed and claws (3) an impressive " small fire" weaponry. They could not even defend themselves (4) running swiftly like the horses, zebras or small animals. If the ape-men had attempted to compete on those terms in the open, they would have been (5) to failure and extinction. But they were (6) with enormous concealed advantages of a kind not possessed by any of their competitors.

In the search (7) the pickings of the forest, the ape-men had (8) efficient stereoscopic vision and a sense of color that the animals of the grasslands did not (9) . The ability to see clearly at close range permitted the ape-men to study practical problems in a way that lay far (10) the reach of the original inhabitants of the grassland. Good long-distance sight was (11) another matter. Lack of long-distance vision had not been a problem for forest-dwelling apes and monkeys because the (12) the viewpoint, the greater the range of sight-so (13) they had had to do was climb a tree. Out in the open, however, this simple solution was not (14) . Climbing a hill would have helped, but in many places the ground was flat. The ape-men (15) the only possible solution. They reared up as high as possible on their hind limbs and began to walk (16) . This vital change of physical position brought about considerable disadvantages. It was extremely unstable and it meant that the already slow ape-men became (17) still. (18) , they persevered and their bone structure gradually became (19) to the new, unstable position that (20) them the name Homo erectus, upright man.

2()

A.match

B.compare

C.rival

D.equal