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高考易错题学生版

高考易错题学生版
高考易错题学生版

例1、 设{}2|8150A x x x =-+=,{}|10B x ax =-=,若A B B =,求实数a 组成的集合的子集有多少个?

【练1】已知集合

{}2|40A x x x =+=、(){}22|2110B x x a x a =+++-=,若B A ?,则实数a 的取值范围是 。

例2、 已知()2

2214

y x ++=,求22x y +的取值范围 【练2】若动点(x,y )在曲线22

214x y b

+=()0b >上变化,则22x y +的最大值为() (A )()()2404424b b b b ?+<

402422b b b b ?+<

(C )244b +(D )2b 例3、 ()2112

x x a f x ?-=+是R 上的奇函数,(1)求a 的值(2)求的反函数()1f x - 【练3】函数

(

)()11f x x =≥的反函数是() A 、

()2221y x x x =-+< B 、()2221y x x x =-+≥ C 、()221y x x x =-< D 、()221y x x x =-≥

例4、已知函数

()121x f x x -=+,函数()y g x =的图像与()11y f x -=-的图象关于直线y x =对称,则()y g x =的解析式为()

A 、()32x

g x x -= B 、()21x g x x -=+ C 、()12x g x x -=+ D 、()32g x x

=+ 【练4】已知函数y=log 2x 的反函数是y=f -1(x),则函数y= f -1(1-x)的图象是()

例5、 判断函数()

2lg 1()22x f x x -=--的奇偶性。

①(

)f x =+()(

1f x x =-()1sin cos 1sin cos x x f x x x

++=+- 【练5】判断下列函数的奇偶性:

例6、 函数()2221211log 22x x f x x x -+??=<-> ???

或的反函数为()1f x -,证明()1f x -是奇函数且在其定义域上是增函数。 【练6】(1)已知()2x x e e f x --= ,则如下结论正确的是()

A 、 ()f x 是奇函数且为增函数

B 、()f x 是奇函数且为减函数

C 、 ()f x 是偶函数且为增函数

D 、 ()f x 是偶函数且为减函数

例7、试判断函数()()0,0b f x ax a b x

=+>>的单调性。 【练7】(1)

()()10x f x ax a ax -=+>(1)用单调性的定义判断函数()f x 在()0,+∞上的单调性。(2)设()f x 在01x <≤的最小值为()g a ,求()y g a =的解析式。

例7、 已知函数()3231f x ax x x =+-+上是减函数,求a 的取值范围。

【练8】(1)函数

2y x bx c =++()()0,x ∈+∞是是单调函数的充要条件是() A 、0b ≥ B 、0b ≤ C 、0b > D 、0b <

(2)是否存在这样的K 值,使函数()243221232

f x k x x kx x =--++在()1,2上递减,在()2,+∞上递增? 例9 甲、乙两地相距s km , 汽车从甲地匀速行驶到乙地,速度不得超过c km/h ,已知汽车每小时的运输成本(以元为单位)由可变部分和固定部分组成:可变部分与速度v (km/h )的平方成正比,比例系数为b;固定部分为a 元。

(1) 把全程运输成本y (元)表示为速度v (km/h )的函数,并指出这个函数的定义域;

(2) 为了使全程运输成本最小,汽车应以多大速度行驶?

例10、是否存在实数a 使函数()2log ax x a f x -=在[]2,4上是增函数?若存在求出a 的值,若不存在,说明理由。

【练10】(1)(黄岗三月分统考变式题)设0a

>,且1a ≠试求函数2log 43a y x x =+-的的单调区间。 (2)若函数()()()3log 0,1a f x x ax a a =->≠在区间1(,0)2

-内单调递增,则a 的取值范围是() A 、1[,1)4 B 、3[,1)4 C 、9(,)4+∞ D 、9(1,)4

例11、已知1sin sin 3

x y +=求2sin cos y x -的最大值 【练11】(1)不等式x >ax +

32的解集是(4,b),则a =________,b =_______。 例12、数列{}n a 前n 项和n s 且1111,3

n n a a s +==。(1)求234,,a a a 的值及数列{}n a 的通项公式。 【练12】已知数列

{}n a 满足()()112311,2312n n a a a a a n a n -==++++-≥则数列{}n a 的通项为 。 例13、等差数列

{}n a 的首项10a >,前n 项和n s ,当l m ≠时,m l s s =。问n 为何值时n s 最大? 【练13】设

{}n a 是等差数列,n s 是前n 项和,且56s s <,678s s s =>,则下列结论错误的是() A 、0d D 、6s 和7s 均为n s 的最大值。

例14、已知关于的方程230x x a -+=和230x x b -+=的四个根组成首项为

34

的等差数列,求a b +的值。 【练14】已知方程220x x m -+=和220x x n -+=的四个根组成一个首项为14的等差数列,则m n -=()

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