2..2函数的定义域和值域(20211204164225).pdf
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1、1/9 本资料来源于七彩教育网http:/ 22 函数的定义域与值域【知识网络】1函数的定义域;2函数的值域【典型例题】例11)函数)13lg(13)(2xxxxf的定义域是 C)A,31)B(31,31)C(31,1)D(31,)提示:由10310 xx解得113x答案为 C.A|1x xB|2x xC|12x xx且D|12x xx或提示:11()1()111ff xf xx,11101xx,解得12xx且,答案为 C3)函数268ykxxk的定义域为 R,则k的取值范围是 B)A.09kk或 B.1k C.91k D.01k提示:2680kxxk恒成立,0k显然不符,0364(8)0kk
2、 k,解得:1k,选 B.12)yxxx;2232xyx;914xyx;xxycottan5)若的最大值是则yxyx43,122_5_ 提示:设cos,sinxy,则343cos4sin5sinxy(),其最大值为5例21)求下列函数的定义域:xxxxxxf02)1(65)(的定义域2)已知函数()f x的定义域是(,)a b,求函数()(31)(31)F xfxfx的定义域解:由函数解读式有意义,得2/9 0010652xxxxx321011230 xxxxxxx或或或故函数的定义域是),32,1()1,0(2)由113133311133abxaxbaxbabx 函数的定义域不可能为空集,必
3、有1133ab,即2ba此时,1133abx,函数的定义域为 3131 ba,);例3求下列函数的值域:1)2432yxx;2)12yxx;3)221223xxyxx;4)35yxx;解:1)24(1)4yx,20(1)44x,20(1)42x224(1)44x所给函数的值域为 2,4,则x=212t212tyt21(1)12t,当1t时,max1y所给函数的值域为(,1.3)由已知得:2(21)(21)(31)0yxyxy*)当210y时,12y,代入*)式,不成立,12y当210y时,则:211312231102(21)4(21)(31)0102yyyyyyy 所给函数的值域为31,)10
4、24)530503xxx得由函数定义域为 3,5 2222(3)(5)22 1(4)yxxx又当4x时,2max4y,当35x或时,2min2y224y0y22y文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R
5、2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1
6、Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8
7、I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10
8、HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6
9、D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编
10、码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V
11、9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R2文档编码:CY10V6D5O7O10 HY4M10N8I3N6 ZJ1Y10V9S8R23/9 所给2,2函数的值域为例 4已知函数2()3yf xxax在区间 1,1 上的最小值为3,求实数a的值解:43)2()(22aaxxfy1)min12(1)432aayfa当,即时,解得:7a2)当112a,即22a时,2mi n()3324aayf,解 得2 6a舍去)3)当12a,即2a时,min(1)43yfa,解得:7a综合1)2)3)可得:a=7【课内练习】1函数23)(xxxf的定义域为 B
12、)A0,错误!B0,3 C3,0 D0,3)zwj2px3C3L 提示:由230 xx得:03x,答案为 B2函数251xyx的值域为 A5|2y y B|0y y C|25y yy且 D2|5y y提示:y)15(5252x,)15(52x 0,y52答案为 D3若函数()f x的定义域为,ab,且0ba,则函数()()()g xf xfx的定义域是 D)A,ab B,ba C,bb D,aa提示:由(0)axbbaaxb得:(0)axbbabxa即axa,答案为D4函数2211xyx的值域为 的值域是2,)提示:24(1)923(1)26(1)32(1)xyxxx,文档编码:CP6I7D1
13、0S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5
14、HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y
15、10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1
16、 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8
17、I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4
18、文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:C
19、P6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S44/9 当且仅当123(1)32(1)xxx即12x时取等号又函数无最大值,故函数值域为2,)7若一系列函数的解读式相同、值域相同,但其定义域不同,则称这些函数为“同族函数”,那么函数解读式为
20、2yx、值域为 1,4 的“同族函数”共有 9 个.zwj2px3C3L 提示:设函数2yx的定义域为 D,其值域为 1,4,D的所有情形的个数,即是同族函数的个数,D的所有情形为:1,2,1,2,1,2,1,2,1,1,2,1,1,2,1,2,2,1,2,1,zwj2px3C3L 1,1,2,2共9个,答案为 98求下列函数的定义域:1)2311xxyx;2)12log(2)xyx解:(2,3 2)由12log(2)0 x,得:021x,即:12x,函数的定义域为(1,2)9求下列函数的值域:1)242(14)yxxx;2)xxysin2sin2;3)22436xxyxx解:1)2(2)2y
21、x14x,当2x时,max2y,当4x时,min2y 所给函数的值域为 2,22)由xxysin2sin2解得:22sin1yxy,由|sin|1x得22|11yy两边平方后整理,得:231030yy,解得:133x,故所给函数的值域为1,33 若1y,代入 得:3x,25y函数的值域为:2|,15y yRyy且评注:本题中需要检验的原因是:函数22436xxyxx可化简为文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3
22、X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5
23、H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1
24、S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码
25、:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7D10S7L5 HP6K7Y10K3X1 ZH5H8I7N1S4文档编码:CP6I7
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