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第Ⅰ卷

一、选择题(每小题5分,共60分)

1.设全集U={1,2,3,4,5,6},集合A={2,4,6},B={1,2,3,5},则 )(A C U B 等于 A .Φ B .{1,3,4,5,6} C .{1,3,5} D .{1,2,3,5}

2.下列函数中,与函数x y =相同的是( )

A .2

x y = B .2)(x y = C .x y 10lg = D .x y lg 10=

3.已知2)(357++-=cx bx ax x f ,且m f =-)5(,则)5()5(-+f f 的值为( ) A.4 B.0 C.m 2 D.4+-m

4.下列函数中,既是偶函数,又在区间)0,(-∞上单调递增的是:

A x x f 2)(=

B x x f 1

)(-= C

1)(2+=x x f D 1)(2

+-=x x f 5.设f (x )是定义在R 上奇函数,且当x >0时,)2(,32)(--=f x f x

则等于( )

A .-1

B .411

C .1

D .-411

6.函数()12-=x x f 的定义域是 ( ) A .}0|{x x D . }0|{≥x x

7.已知a >0且a ≠1,则两函数f (x )=a x 和g (x )=log a (-x )的图像只可能是

(

)

8.设a >l ,则0.2log 0.2a a 、与0.2a 的大小关系是( ) A .0.20.2log 0.2a a a << B .0.20.2log 0.2a a a << C .0.20.20.2log a a a << D .0.20.20.2log a a a <<

9.已知()x x f +=1-1,则()x f 的表达式为( )

()x x f -=2 B.()x x f +=2 C.()2-=x x f D.()1+=x x f

10.若二次函数c bx x x f ++=2)(的图像的对称轴是直线2=x ,则( ) A .)4()2()1(f f f << B .)4()1()2(f f f << C .)1()4()2(f f f << D .)1()2()4(f f f <<

11.根据表格中的数据,可以断定方程20x e x --=的一个根所在的区间是

A 12.已知(31)4,1()log ,1a a x a x f x x x -+?

是(,)-∞+∞上的减函数,那么a 的取值范围是

( ) (A )(0,1)

(B )1(0,)3 (C )11[,)73 D )1

[,1)7 第Ⅱ卷 二、填空题(每小题5分,共20分)

13.若幂函数()y f x =的图像经过点19,3??

???

, 则()25f 的值是 .

14.若函数8y ax =+与12y x b =-+是互为反函数,则a =_____=b _____. 15.用“二分法”求方程2370x

x +-=在区间[1,3]内的根,取区间的中点为02x =,

那么下一个有根的区间是 _______

16.某同学在研究函数()()

1||x

f x x R x =∈+时,分别给出下面几个结论:

①等式()()0f x f x -+=对x R ∈恒成立;

②函数()f x 的值域为(1,1)-;

③若12x x ≠,则一定有12()()f x f x ≠;

④函数()()g x f x x =-在R 上有三个零点.

其中正确结论的序号有________________(请将你认为正确的结论的序号都填上) 三、解答题(第17题10分,其余每小题12分)

17.(1)已知A={2,3},B={x |20x ax b ++=},且AB={2},AB={2,3},求a +b

(2)210

23213(2)(9.6)(3)(1.5)48-----+

(3

)231

lg 25lg 2log 9log 22

+-?

18.已知二次函数2483y x x =-+-。

(1)指出图像的开口方向、对称轴方程、顶点坐标;

(2)画出它的图像,并说明其图像由24y x =-的图像经过怎样平移得来; (3)求函数的最大值或最小值;

(4)写出函数的单调区间(不必证明)。

19.若函数)(x f =122

-+ax x 的图像过点)2,1( (1)求函数)(x f 的解析式 ;

(2)求函数)(x f 在区间]2,2[-上的最小值和最大值. 20.已知函数()log (1)log (3)(01)a a f x x x a =-++<< (1)求函数()f x 的定义域;

(2)求函数()f x 的零点;

(3)若函数()f x 的最小值为-4,求a 的值。

21.已知函数2()2x x b f x a

+=+,且1

(1)3f =,(0)0f =

(1)求函数()f x 的解析式;

(2)判断函数()f x 在定义域上的单调性,并证明; (3)求证:方程()ln 0f x x -=至少有一根在区间()1,3.

22.某公司要将一批不易存放的蔬菜从A 地运到B 地,有汽车、火车两种运输工具

x km

(I )设采用汽车与火车运输的总费用分别为()f x 与()g x ,求()f x 与()g x ; (II )试根据A 、B 两地距离大小比较采用哪种运输工具比较好(即运输总费用最小). (注:总费用=途中费用+装卸费用+损耗费用)

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