(完整word版)高中数学函数的单调性练习题及其答案.pdf

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1、-1 函数的单调性一、选择题：1在区间(0，)上不是增函数的函数是（）Ay=2x1 By=3x21 Cy=x2D y=2x2x1 2函数 f(x)=4x2mx5 在区间 2，上是增函数，在区间(，2)上是减函数，则 f(1)等于（）A 7 B1 C17 D 25 3函数 f(x)在区间(2，3)上是增函数，则y=f(x5)的递增区间是（）A(3，8)B(7，2)C(2，3)D(0，5)4函数 f(x)=21xax在区间(2，)上单调递增，则实数a 的取值范围是（）A(0，21)B(21，)C(2，)D(，1)(1，)5已知函数f(x)在区间 a，b上单调，且 f(a)f(b)0，则方程f(x)

2、=0 在区间 a，b内（）A至少有一实根B至多有一实根C没有实根D必有唯一的实根6已知函数f(x)=82x x2，如果 g(x)=f(2x2)，那么函数g(x)（）A在区间(1，0)上是减函数B在区间(0，1)上是减函数C在区间(2，0)上是增函数 D在区间(0，2)上是增函数7已知函数f(x)是 R 上的增函数，A(0，1)、B(3，1)是其图象上的两点，那么不等式|f(x1)|1 的解集的补集是（）A(1，2)B(1，4)C(，1)4，）D(，1)2，）8已知定义域为R 的函数 f(x)在区间(，5)上单调递减，对任意实数t，都有 f(5t)f(5t)，那么下列式子一定成立的是（）Af(1

3、)f(9)f(13)Bf(13)f(9)f(1)Cf(9)f(1)f(13)D f(13)f(1)f(9)9函数)2()(|)(xxxgxxf和的递增区间依次是（）A 1,(,0,(B),1,0,(C1,(),0D),1),0-2 10已知函数2212fxxax在区间4,上是减函数，则实数a的取值范围是（）Aa3 Ba 3 Ca5 Da3 11已知 f(x)在区间(，)上是增函数，a、bR 且 ab0，则下列不等式中正确的是（）Af(a)f(b)f(a)f(b)Bf(a)f(b)f(a)f(b)Cf(a)f(b)f(a)f(b)D f(a)f(b)f(a)f(b)12定义在 R 上的函数 y=

4、f(x)在(，2)上是增函数，且 y=f(x2)图象的对称轴是 x=0，则（）Af(1)f(3)Bf(0)f(3)Cf(1)=f(3)Df(2)f(3)二、填空题：13函数 y=(x1)-2的减区间是 _ _14函数 y=x2x1 2 的值域为 _ _15、设yfx是R上的减函数，则3yfx的单调递减区间为.16、函数 f(x)=ax24(a1)x3 在2，上递减，则 a 的取值范围是_ 三、解答题：17f(x)是定义在(0，)上的增函数，且f(yx)=f(x)f(y)（1）求 f(1)的值（2）若 f(6)=1，解不等式f(x3)f(x1)2 18函数 f(x)=x31 在 R 上是否具有单

5、调性？如果具有单调性，它在R 上是增函数还是减函数？试证明你的结论19试讨论函数f(x)=21x在区间 1，1上的单调性文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1

6、A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG

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8、R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10

9、T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:

10、CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 H

11、Y8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8-3 20设函数 f(x)=12xax，(a 0)，试确定：当a 取什么值时，函数f(x)在 0，)上为单调函数21已知 f(x)是定义在(2，

12、2)上的减函数，并且f(m1)f(12m)0，求实数 m 的取值范围22已知函数f(x)=xaxx22，x 1，（1）当 a=21时，求函数f(x)的最小值；（2）若对任意x 1，)，f(x)0 恒成立，试求实数a 的取值范围文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I

13、7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A

14、6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2

15、U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R

16、3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T

17、1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:C

18、G2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8-4 参考答案一、选择题：CDBBD

19、ADCCA BA 二、填空题：13.(1，)，14.(，3)，15.3,，21,三、解答题：17.解析：在等式中0yx令，则 f(1)=0在等式中令x=36，y=6 则.2)6(2)36(),6()36()636(fffff故原不等式为：),36()1()3(fxfxf即 fx(x3)f(36)，又 f(x)在(0，)上为增函数，故不等式等价于：.23153036)3(00103xxxxx18.解析：f(x)在 R 上具有单调性，且是单调减函数，证明如下：设 x1、x2(，)，x1x2，则 f(x1)=x131，f(x2)=x231f(x1)f(x2)=x23x13=(x2x1)(x12x1x

20、2x22)=(x2x1)(x122x)243x22 x1x2，x2x10 而(x122x)243x220，f(x1)f(x2)函数 f(x)=x31 在(，)上是减函数19.解析：设 x1、x2 1，1且 x1x2，即 1x1x21f(x1)f(x2)=211x221x=2221222111)1()1(xxxx=2221121211)(xxxxxxx2x10，222111xx0，当 x10，x20 时，x1x20，那么 f(x1)f(x2)当 x10，x20 时，x1x20，那么 f(x1)f(x2)故 f(x)=21x在区间 1，0上是增函数，f(x)=21x在区间 0，1上是减函数20.解

21、析：任取x1、x20，且 x1x2，则f(x1)f(x2)=121x122xa(x1x2)=1122212221xxxxa(x1x2)文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6

22、 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8

23、文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W

24、6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5

25、T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4

26、G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U

27、8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8-5=(x1x2)(11222121xxxxa)(1)当 a 1 时，11222121xxxx1，又 x1x20，f(x1)f(x

28、2)0，即 f(x1)f(x2)a1 时，函数f(x)在区间 0，)上为减函数(2)当 0 a1 时，在区间 0，上存在x1=0，x2=212aa，满足 f(x1)=f(x2)=1 0a1 时，f(x)在，上不是单调函数注：判断单调性常规思路为定义法；变形过程中11222121xxxx1 利用了121x|x1|x1;122xx2；从 a 的范围看还须讨论0 a1 时 f(x)的单调性，这也是数学严谨性的体现21.解析：f(x)在(2，2)上是减函数由 f(m1)f(12m)0，得 f(m1)f(12m)32232131211,2212212mmmmmmm即解得3221m，m 的取值范围是(32

29、,21)22.解析：(1)当 a=21时，f(x)=xx21 2，x1，)设 x2x11，则 f(x2)f(x1)=x21122121xxx=(x2x1)21212xxxx=(x2x1)(12121xx)x2x11，x2x10，12121xx0，则 f(x2)f(x1)可知 f(x)在 1，)上是增函数f(x)在区间 1，)上的最小值为f(1)=27(2)在区间 1，)上，f(x)=xaxx220 恒成立x2 2xa0 恒成立设 y=x2 2xa，x1，)，由 y=(x1)2a 1 可知其在 1，)上是增函数，当 x=1 时，ymin=3a，于是当且仅当ymin=3a0 时函数 f(x)0 恒

30、成立故a 3文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG

31、2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8

32、R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10

33、T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:

34、CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 H

35、Y8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8文档编码:CG2U1U8W6S4 HY8R3I7G5T6 ZD10T1A6T4G8