**NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions: **Going through the NCERT solutions is a crucial part of your preparation for Class 12 board exams, JEE (Main and Advanced) and other exams. This will clear your doubts in regards to any question and improve your application skills. In this article, we will provide you with NCERT Solutions for Class 12 Maths – Chapter 1 – Relations and Functions. Read on to find out.

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### NCERT Solutions for Class 12 Maths Relations and Functions – Important Questions

Important 4 Mark Questions of Relations and Functions1. Functions f ,g :R →R are defined, respectively, by f(x) = x^{2} + 3x +1, g(x) = 2x − 3, find(i) fog(ii) gof(iii) fof(iv) gog 2. Let * be the binary operation defined on Q. Find which of the following binary operations are commutative. 3. Let R be relation defined on the set of natural number N. Find the domain and range of the relation. Also verify whether R is reflexive, symmetric and transitive.4. Given, A= {2,3,4} ; B= {2,5,6,7} . Construct an example of each of the following:(i) an injective mapping from a to B.(ii) a mapping from a to b which is not injective.(iii) a mapping from b to A. 5. Let a ={1, 2, 3, …,9} and R be the relation in A× a defined by (a , b) R (c , d) if a + d = b + c for (a , b), (c , d) in a × a Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]. 6. Let A = [-1,1] , then, discuss whether the following functions defined on A are one-one onto or bijective.(i) f(x) = x/2(ii) g(x) = |x|(iii) h(x) = x |x|(iv) k(x) = x^{2} |

### NCERT Solutions for Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths – Chapter 1 – Relations and Functions as provided by India’s best teachers will give detailed and step-wise solutions to all the questions at the end of the chapter from the NCERT Maths book. The concepts included in the Relations and Functions chapter are tabulated below:

Ex 1.1 | Introduction |

Ex 1.2 | Types of Relations |

Ex 1.3 | Types of Functions |

Ex 1.4 | Composition of Functions and Invertible Function |

Ex 1.5 | Binary Operations |

** NCERT Solutions For Class 12 Maths Chapter 1 Relations and Functions Description**

The concept of the term ‘**relation**’ in mathematics has been drawn from the meaning of relation in English language, according to which two objects or quantities are related if there is a recognisable connection or link between the two objects or quantities. Let **A** be the set of students of Class XII of a school and** B** be the set of students of Class XI of the same school. Then some of the examples of relations from **A to B** are

- {(a, b) ∈ A × B: a is brother of b},
- {(a, b) ∈ A × B: a is sister of b},
- {(a, b) ∈ A × B: age of a is greater than age of b},
- {(a, b) ∈ A × B: total marks obtained by a in the final examination is less than the total marks obtained by b in the final examination},
- {(a, b) ∈ A × B: a lives in the same locality as b}.

However, abstracting from this, we define mathematically a relation R from A to B as an arbitrary subset of A × B. If (a, b) ∈ R, we say that a is related to b under the relation R and we write as **a** R **b**. So as you learnt in Class 11, the functions are special kind of relations whereas in this Class 12 Chapter 1, you will learn about different types of relations and functions, the composition of functions, invertible functions and binary operations.

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