Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ The relation g is defined as g x x 2 , 0 x2 3 x, 2 x10 It can be observed that for 2 x 2, g x 2 4 and g x 3 2 6 Hence, element 2 of the domain of the relation g corresponds to two different images i.e., 4 and 6. Hence, this relation is not a function. Question 2: If 2 , f x x Solution 2: 2 f x x find f 1.1 f 1 1.**11** 2 2 f 1.1 f 1 1.1 1 1.2**11** 0.21 2.1 1.**11** 1.**11** 0.1 01 Question 3: Find the domain of the function Solution 3: The given function is f x f x 2 2 x x x x 2 x x x x f x 2 x 2x1 2 x 8x12 2 1 2 1 8 12 6 2 2 x 2x1 2 x 8x12 It can be seen that function f is defined for all real numbers except at x = 6 and x = 2. Hence, the domain of f is 2,6 R . 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 ______________________________________________________________________________ Question 4: Find the domain and the range of the real function f defined by Solution 4: The given real function is It can be seen that x 1 f x x 1 is defined for 1. f x x f x x 1 Therefore, the domain of f is the set of all real numbers greater than or equal to 1 i.e., the domain of As f 1, . x 1 x 1 0 x 1 0 Therefore, the range of f is the set of all real numbers greater than or equal to 0 i.e., the range of f 0, . Question 5: Find the domain and the range of the real function f defined by f x x 1 . Solution 5: The given real function is It is clear that Domain of Also, for x 1 f R x R x1 1 f x x is defined for all real numbers. assumes all real numbers. Hence, the range of f is the set of all non-negative real numbers. . Question 6: Let 2 x f x, : x R 2 1 x be a function from R into R. Determine the range of f. Solution 6: 2 x f x, : x 2 R 1 x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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