Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 11 Mathematics 2. Relations and Functions to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 11 Mathematics 2. Relations and Functions to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 2.3. Whether you are studying for board exams or mid-term exams, 11 Mathematics Chapter 2. Relations and Functions solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 2.3
Q1. 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:
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Let be R = {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
There is no same component in the domain of given relation, so this relation is a function.
Here, domain = {2, 5, 8, 11, 14, 17} and range = {1}
Solution:
(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Let be R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
There are also unique domain components or order pair in the given relation, so this relation is a function.
Here, domain = {2, 4, 6, 8, 10, 12, 14} and range = {1, 2, 3, 4, 5, 6, 7}
Solution:
(iii) {(1, 3), (1, 5), (2, 5)}
Since the domain has the same first element i.e., 1 corresponds to two different images i.e.,
3 and 5, this relation is not a function.
Q2. Find the domain and range of the following real functions:
(i) f(x) = – |x|
Solution2:
Q3: A function f is defined by f(x) = 2x – 5
(i) f (0) (ii) f(7) (iii) f(-3)
Solution 3:
The given function is f(x) = 2x – 5
Therefore,
(i) f(0) = 2 × 0 – 5 = 0 – 5 = - 5
(ii) f(7) = 2 × 7 – 5 = 14 – 5 = - 9
(iii) f(-3) = 2 × -3 – 5 = -6 – 5 = - 11
Solution:
Solution:
(iii) f(x) = x is real number.
It is clear that the range of f is the set of all real number.
Therefore, range of f = R
Exercise 2.3 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 11 Mathematics Chapter 2. Relations and Functions solutions help you understand the core concepts and practice effectively.
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Our Exercise 2.3 are useful for both board exams and mid-term exams. For 11 Mathematics, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 2.3 for 11 Mathematics Chapter 2. Relations and Functions are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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