Important Questions for Class 12 Maths Chapter 1 – Relations and Functions

1) Let A = {1, 2, 3}, S = {4, 5, 6, 7}, and f = {(1, 4), (2, 5), (3, 6)} represent a function from A to S. Find if f is one-one or not.

Ans – Given A = {1, 2, 3} and B = {4, 5, 6, 7}.
The function f: A → B is defined as f = {(1, 4), (2, 5), (3, 6)}
⇒ f(1) = 4, f(2) = 5, and f(3) = 6.
The images of distinct elements of A under f are unique. Thus, f is one-one.

Ans – First, use the modulus definition to redefine the function, i.e. by using

We can simplify further to get the range.

6) Let f : N → Y be a function defined by f(x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3 for some x ∈ N}. Prove that the function f is invertible. Find its inverse.

Ans – Given f: N → Y be defined by f(x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3, x ∈ N}.
For any arbitrary element y ∈ Y, it follows that y = 4x + 3 for some x ∈ N.

7) Let f and g be two functions defined on the real numbers, where f(x) = |x| + x and g(x) = |x| – x for all x in R. Then, find out fog and gof.

NCERT Questions for Class 12 Maths Chapter 1 – Relations and Functions

In the context of mathematics, Relations and Functions form the basic idea through which the knowledge is presented to students in the higher classes like class 12. The basis for many more complex ideas of calculus, algebra, and geometry forms with the understanding of Relations and Functions. Therefore, a deep understanding of Relations and Functions will enable the student to master other academic subjects also.

Importance of Relations and Functions in Class 12

Relations and Functions are the interrelated mathematical concepts that assist in understanding the relationship between two sets of elements. In class 12, students learn in detail about the various types of relations, which include reflexive, symmetric, transitive, and equivalence relations. In addition, functions are learned in great detail, such as one-to-one, onto, and invertible functions.

Relations and Functions are the knowledge areas that prepare students to reason critically and have a better potential for solving various problems. For class 12 students, mastering these topics through important questions of Relations and Functions is a core part of mathematical learning. For instance, having a proper and strong understanding of Relations and Functions helps students cope with more critical topics in Calculus and algebra.

Importance of Important Questions

It is necessary to master any subject by practicing essential questions to help students learn concepts and solve problems successfully. Important questions guide the mind of a student, helping to focus on the probable topics that would be dealt with in an examination. While solving important questions, one can realize or identify areas of his own strength and weaknesses, thus, he can focus on improvements accordingly.

Important questions on Relations and Functions for class 12 students serve as a source of revisiting the basic concepts and strengthening the understanding of the topic. A wide range of concepts, starting from basic definitions to advanced techniques of problem solving, are included in these important questions, hence providing a very comprehensive review of the subject matter. Regular practice of important questions helps students enhance their confidence and performance in the exams.