Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ 1 1 9 4 9 16 0,0 , 0.5, , 1, , 1.5, , 2, , 3, , 4, ,.... 5 2 13 5 10 17 The range of f is the set of all second elements. It can be observed that all these elements are greater than or equal to 0 but less than 1. [Denominator is greater numerator]. Thus, range of f = [0, 1) Question 7: Let f g . f, g: R R Solution 7: f, g: R R be defined , respectively by is defined as f x x 1, g x 2x 3 f g x f x g x x 1 2x 3 3x 2 f g x 3x 2 f x x 1, g x 2x 3 f g x f x g x x 1 2x 3 x 1 2x 3 x 4 f g x x 4 f g f x x , g x 0, x R g x f x1 x ,2 x 3 0 or 2 x 3 g 2x 3 f x1 3 x , x g 2x3 2 . Find f g, f g and Question 8: Let 1,1 , 2,3 , 0, 1 , 1, 3 f some integers Solution 8: ab , . Determine 1,1 , 2,3 , 0, 1 , 1, 3 f ab , 1,1 f f 1 1 a 1 b 1 ab 1 . and be a function from Z to Z defined by f x ax b f x ax b , for Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ 0, 1 f f 0 1 a 0 b 1 On substituting b 1 in a b 1 We obtain a 1 1 a **11** 2 . Thus, the respective values of a and b are 2 and 1. Question 9: Let R be a relation from N to N defined by true? a, a R, (i) a, b R, (ii) (iii) for all aN b, a implies a, b R, b, c R R a, c implies Justify your answer in each case. Solution 9: R a, b : a, bN and a b 2 R (i) It can be seen that 2N ; however, Therefore, the statement , for all (ii) It can be seen that 3,9 N Therefore, the statement " a, a R 9,3 N " a, b R, 9,3 R, 16, 4 . R a, b : a, bN and a b . aN"is not true. 2 2 2 4 because (iii) It can be seen that 2 Now, 9 4 16 ; therefore, Therefore, the statement 9,4 N implies R " a, b R, b, c R 9,3 N and " b, a R" 2 9 3 . Now, is not true. because 9,3,16,4 N implies a, c R" and 2 . Are the following 2 3 9 81; 2 9 3 is not true. and therefore, 2 16 4 . Question 10: Let A 1, 2,3, 4 , B 1,5,9,**11**,15,16 following true? (i) f is a relation from A to B (ii) f is a function from A to B Justify your answer in each case. Solution 10: and f 1,5 , 2,9 , 3,1 , 4,5 , 2,**11** . Are the Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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