(iv) Composition (Function of Function) Let f : A → B and g : B → C be two functions. g y y Maths MCQs for Class 12 Chapter Wise with Answers, Teenage Pregnancy Essay | Essay on Teenage Pregnancy for Students and Children in English, Animal Right Essay | Essay on Animal Right for Students and Children in English, Water Conservation Slogans | Unique and Catchy Water Conservation Slogans in English, Slogans on Pollution | Unique and Catchy Slogans on Pollution in English, Maths Formulas for Class 11 PDF Download Free | 11th Std Maths Formulae List, Maths Formulas for Class 6 | List of 6th Class Math Formulae, Maths Formulas for Class 9 PDF Free Download | Important 9th Grade Maths Formulae, Maths Formulas for Class 8 PDF Download Free | 8th Grade Math Formula List, Maths Formulas for Class 7 PDF Download Free | 7th Class Math Formulae, Basic Chemistry Formulas Sheet | Important Chemistry Formula Chart & Tables, https://www.youtube.com/watch?v=nd-0HFd58P8. i.e., Range ⊂ Codomain. function. − 3 Let A and B be .two non-empty sets, then a function f from set A to set B is a rule whichassociates each element of A to a unique element of B. ... Download NCERT Solutions for Class 12 Chapter 1 Relations and Functions. We define g : B → A, such that f(x) = y => g(y) = x, g is called inverse of f and vice-versa. R = {(P, Q) : distance of the point P from the origin is same as the distance of the (D) R is an equivalence relation. (i) Put f(T + x) = f(x) and solve this equation to find the positive values of T independent of x. (b) R = {(x, y) : x and y live in the same locality} NCERT Solutions for Class 12 Maths Chapter-1 PDF is now available for download on the official website of Vedantu. %PDF-1.4 Question 10. . Question 5. 0000008434 00000 n Link of our facebook page is given in sidebar. = (ii) Implicit Functions A function is said to be an implicit function, if it is expressed in the 0000007291 00000 n (B) Is commutative but not associative? (ix) [x + y] = [x] + [y + x – [x}] for all x, y ∈ R Range of f(x) = R – {0}, Modulus function is given by y = f(x) = |x| , where |x| denotes the absolute value of x, that is, Domain of f(x) = R (ii) g : {5, 6, 7, 8} → {1, 2, 3, 4} with (iv) Relation R in the set Z of all integers defined as 112 0 obj <> endobj inverse of f. Question 8. Range f(x) = R. If a and b be fixed real numbers, then the linear function is defmed as y = f(x) = ax + b, where a (ii) On Z+, define by a b = ab Question 14.Let L be the set of all lines in XY plane and R be the relation in L defined as (i) Explicit Functions A function is said to be an explicit function, if it is expressed in the form (A) R is reflexive and symmetric but not transitive. (C) R is symmetric and transitive but not reflexive. 0000005901 00000 n <]>> Ncert Math Notes For Class 12 Chapter 1 Relations And Functions Download PDf. (v) Odd function * Odd function = Even function. − , (i) Even function ± Even function = Even function. ∴ is reflexive. In case, the domain of f function, then d / dx f(x) or ∫ f(x) dx is even. related to each other. (x) [x + y] ≥ [x] + [y] Let f : X → Y be an invertible function. (ix) tann x and cotnx are periodic functions with period π. (iii) Irrational Functions The algebraic functions containing one or more terms having nonintegral %PDF-1.4 %���� Odd Functions A real function f(x) is an odd function, if f( -x) = – f(x). (4 3) Hence, is reflexive and transitive but not symmetric. operation? Question 5.Show that the Signum Function f : R→R, given by Relations and Functions Class 12 Maths MCQs Pdf. (vii) |sin x|, |cos x|, |tan x|, |cot x|, |sec x| and |cosec x| are periodic functions with period π. endobj (xi) An even function can never be one-one, however an odd function mayor may not be oneone. h = {(2, 7), (3, 9), (4, 11), (5, 13)}, Question 6. Question 9. Show that the relation R in the set A of all the books in a library of a college, w�g��p���&����e��\}�i�Zô�� ����宥&�s0��[�<0 Answer/Explanation. (C) (6, 8) ∈ R ∴R is not reflexive. (vi) gof or fog is even, if anyone of f and g or both are even. (iii) Compute (2 3) (4 5). Let f : N → N be defined by f (n) = Question 1.Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by Question 11. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. –1, if 0 Range of f(x) = (0, ∞), Domain of f(x) = R – {0} (ii) Transitive but neither reflexive nor symmetric. 0000013697 00000 n and semi-closed intervals. Is the operation ′ same as the operation defined = Show that none of the operations given above has identity. 1 (iii) Period = 2π, (i) Domain = R ~ (2n + 1) π / 2, n ∈ I Even Functions A real function f(x) is an even function, if f( -x) = f(x). x a < 1. Question 3.Prove that the Greatest Integer Function f : R→R, given by f (x) = [x], is neither (6 4) fog1(y) = 1Y(y) = fog2(y). 0000011320 00000 n Consider f : R+→ [4, ∞) given by f (x) = x2 +4..Show that f is invertible with the 2 In Chapter 1, you have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto.There are many functions which are not one-one, onto or both and hence we can not talk of their inverses. (C) f is one-one but not onto which is increasing, if a > 1 and decreasing, if 0 < (ii) Graphically If any .line parallel to x-axis cuts the graph of the function atmost at one point, &��:�/�W5���Ktr�9ٳ)?�'�(��j~_&�J�����U��g[��Ka�r��=�u��:���� �Ny�Y`���1ȝ������\2��hY�Ng�z� ��t7 Let R be a relation on the set L of lines defined by l 1 R l 2 if l 1 is perpendicular to l 2, then relation R is (a) reflexive and symmetric (b) symmetric and transitive