Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ Exercise 2.3 Question 1: Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) 2,1 , 5,1 , 8,1 , **11**,1 , 14,1 , 17,1 (ii) 2,1 , 4, 2 , 6,3 , 8, 4 , 10,5 , 12,6 , 14,7 (iii) 1,3 , 1,5 , 2,5 Solution 1: 2,1 , 5,1 , 8,1 , **11**,1 , 14,1 , 17,1 Since 2, 5, 8, **11**, 14 and 17 are the elements of the domain of the given relation having their unique images, this relation is a function. Here, domain (ii) 2,1 , 4, 2 , 6,3 , 8, 4 , 10,5 , 12,6 , 14,7 2,5,8,**11**,14,17 and range 1 Since 2, 4, 6, 8, 10, 12 and 14 are the elements of the domain of the given relation having their unique images, this relation is a function. Here, domain 2, 4,6,8,10,12,14 (iii) 1,3 , 1,5 , 2,5 and range 1, 2,3, 4,5,6,7 Since the same first element i.e., 1 corresponds to two different images i.e., 3 and 5, this relation is not a function. Question 2: Find the domain and range of the following real function: (i) f x x Solution 2: (i) , f x x x R (ii) 2 f x 9 x x, if x 0 We know that x x if x 0 x, if x 0 f x x x, if x 0 Since f(x) is defined for xR , the domain of f is R . It can be observed that the range of is all real numbers except positive real numbers. The range of f is ,0 . f x x 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 ______________________________________________________________________________ (ii) 2 f x 9 x Since is defined for all real numbers that are greater than or equal to 3 and less than or equal to 3, the domain of x: 3 x 3 3,3 . 2 9 x f x is or For any value of x such that 3 x 3, the value of The range of f x is x: 0 x3 or 0,3 . f x will lie between 0 and 3. Question 3: A function f is defined by (i) f 0 , (ii) Solution 3: The given function is Therefore, (i) (ii) 2 5 f x x f 7 2 5 f x x f 0 20 5 0 5 5 f 7 27 5 14 5 9 (iii) f 3 23 5 6 5 **11** . (iii) f 3 Question 4: The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by (i) t (0) 9C f C 32 5 . Find (ii) (iv) The value of C, when tC 212 Solution 4: The given function is Therefore, (i) t t 28 9C f C 32 . 5 9 0 0 32 0 32 32 5 (iii) 928 252 160 412 (ii) t 28 32 5 5 5 910 (iii) t 10 32 92 32 18 32 14 5 t C (iv) It is given that 212 t 10 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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