funktsiya yoki akslantirish bo‘ladi, shunga ko‘ra :
1) Dl (R)={1,2,3} A, Dr (R)={a,b,d} B;
2) (1,a) R, (1,b) R ekanligidan a=b ekanligi kelib chiqishi lozim edi, lekin
a b, chunki to‘plamda bitta element faqat bir marta qatnashadi, B to‘plamda
esa ushbu elementlar alohida-alohida berilgan. Demak R munosabat funksiya
bo‘la olmaydi.
Analitik, grafik ko‘rinishda berilgan funksiyalarni
in’yektivlik, syur’yektivlik, biyektivlikka tekshirish.
Quyidagicha aniqlangan fi(x):[0;+1]→[0;+1] funksiyalar in‘yektiv bo‘ladimi? Syur‘yektiv bo‘ladimi? Biyektiv bo‘ladimi? Javoblaringizni isbotlang?
1![](data:image/png;base64,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) ![](data:image/png;base64,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) .8.0. 1.8.1. 1.8.2
1![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI0AAACKCAIAAAAYOV5KAAAACXBIWXMAAA7DAAAOxQGRNQ/iAAAEZklEQVR4nO2dMVLrMBCGYYaCMiVDkUkJpwBOQTpIBem4QZKK4QZ0kCpnSEW6UHKElJSU6XiaJ0Yx9lpJhK3dlf6v8BjHk2j08UvryOCj7+/vAyCeI/Lo19dXp9OJ2xLgg/C0Xq+vrq6Wy+Xx8XH8BgESwtPz8/PHx4fZPjw8RG8PoCl7MmF6enoyO2Z7f3+PSAmh7MnE6PPz0+yYLSIlh1+eXJgsiJQcfnlyYbIgUnLYeCqFyYJICWHjabVa3d3dVc8wx8/OziI2CRBsPBkZ4/HY7o//w9IgQEJ/HwGkAU86gCcdwJMO4EkH8KQDeNIBPOkAnnQATzqAJx388nR4eIjbj2Ty48kY4m0H8PPjycYItsRCz0/T6XQymdj90Whk1zjMFgftwX6/3+v1Yi6f0p5ubm6q60/kopSug6UJOPg9B4PBxcXF7e3tQSxQ7+kAnnQATzqApxBeXl4ifyI86WDjyV484SsJmWw8Qc/uoC4HNPCkA3jSATyFgLoc0MCTDuApBNTlgAaedABPOoCnEFCXAxp40gE8hZB1XW4XwPzLK3XLY8kvm0nxZDvaf6Nn8jI8SPFk8WjwS7KOE7YowtPWLpbmILu63A10HhPuJXeyGyFFyWsVZk9OQKnHSQ3uZGnxigD/uEdKckfIyoJdUtZ1uaV6e9ouVpL/iyBZnkpJqhpy5Xv1JfaQtQp/HbF7/2Y4LTlk5clDaWTbmrxWya4ur6Pa9cUfi/uZhIzBU/F6qCpjrwujTCQdcOXJI4M0J+271yzq8n07t+78TJJkETo/gRLwpAN4CgF1OaCBJx3AUwhZ1OUgAHjSATzpAJ5CQF3eLqenp+v1WuNjx3LxZPRMJpNutwtPcnl/fx8Oh9fX18vlspE3RF3eMDZGi8ViNpupfnpfyp4ajxEjaXpKJkaOBD1FiBHq8j+RXowc6XhKaTaqkoKn+DFy/3w+wmdZ1HtKO0YOxZ4Sno2qaPWUSYwc+jxJiFHMmcmizFNuMXKo8SQhRozo8CQtRqjLy2QeI4doT9JixIhQT4hRCYme5Mco97ocMapDkCf5MWJEhCd1McqxLkeMdoHTk7oYMcLmCTHaCwZPCcQo/bocMQojnqcEYsRIJE+JxSjBuhwxaoR2PSUWI0ba8oQYNUsrnpKPkfq6HDFqiSY9JR8jRprxlFuMVNbliFEE/uQptxgxEu4JMYpJiCfESEFdjhixsIcnxIiRXT0hRkXaqMtXq1Wv16t7dbsnxCgOr6+v0+l0NBqR/45niyfEKCYmUoPBwKSiaqvWE2LEBWmL9vT4+GjOs/vn5+dx2qcO10Vt4Gy9vb2ZeYv2NJ/PT05OEKOYmKqkJN6EyUTKFhe0p8vLy/YbBmopGrLw37cMilQNWeBJCmYMM5LqLqFqPeX2wGd2/HMN7cnzaDrgiNk5hKfSM4ahqkr8xypjfgrBDTbRPhGedABPOoAnHcCTDuBJB4SnYi2OolwIdJ72fc46aJvacQ+G/Njf42jjzT8F6pQhzvf1VwAAAABJRU5ErkJggg==) .8.3. 1.8.4. 1.8.5.
1.8.6. (-∞;+∞)x(-∞;+∞) dekart ko‘paytmada aniqlangan in‘yektiv ham, syur’yektiv ham bo‘lmagan funksiyaga misol keltiring va isbotlang?
1.8.7. (-∞;+∞)x(-∞;+∞) dekart ko‘paytmada aniqlangan in‘yektiv bo‘lgan, syur’yektiv bo‘lmagan funksiyaga misol keltiring va isbotlang?
1.8.8. (-∞;+∞)x(-∞;+∞) dekart ko‘paytmada aniqlangan in‘yektiv bo‘lmagan, syur’yektiv bo‘lgan funksiyaga misol keltiring va isbotlang?
1.8.9. (-∞;+∞)x(-∞;+∞) dekart ko‘paytmada aniqlangan in‘yektiv ham, syur’yektiv ham bo‘lgan funksiyaga misol keltiring va isbotlang?
Quyidagicha aniqlangan fi(x):(-∞;+∞)→(-∞;+∞) funksiyalar in‘yektivlik, syur’yektivlik, biyektivlikka tekshirilsin:
1.8.10. f1(x)=x2 1.8.11. f2(x)=lnx 1.8.12. f3(x)=x*sinx
1.8.13. f4(x)=tgx 1.8.14. f5(x)=2x+1 1.8.15. f6(x)=sinx
1.8.16. f7(x)=cosx 1.8.17. f8(x)=ctgx 1.8.18. f9(x)=ax
1.8.19. f10(x)=logax 1.8.20. f11(x)=2*x+1 1.8.21. f12(x)=x3
1.8.22. f13(x)=1/x 1.8.23. f14(x)=1/(x+1) 1.8.24. f15(x)=x3-4x
0- topshiriqlarning ishlanishi:
1.8.0. Topshiriqda grafik ko‘rinishda berilgan f1(x) [0;1]x[0;1]=AxB munosabatni funksiyaga tekshiramiz:
1) Dl(f1)=[0;0.5] A, Dr(f1)=[0;1]=B
2) , ekanligidan ekanligi kelib chiqadi, ya’ni bitta
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