NCERT solutions for class 11 Maths exercise 2.3 chapter 2 Relations and Functions
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions are solved here for helping the students of 11 class maths students to clear their doubts on solving the NCERT unsolved questions of class 11 maths exercise 2.3 of chapter 2 Relations and functions. The proper understanding of exercise 2.3 is needed for every student for attempting the questions of higher class maths. All NCERT solutions of exercise 2.3 are prepared by an expert of maths who has huge experience in maths teaching. Each solution of the maths question is explained beautifully in easy language, therefore, every student can understand it.
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NCERT solutions for class 11 Maths exercise 2.3 chapter 2 Relations and Functions
NCERT solutions of class 11 maths
Chapter 1-Sets | Chapter 9-Sequences and Series |
Chapter 2- Relations and functions | Chapter 10- Straight Lines |
Chapter 3- Trigonometry | Chapter 11-Conic Sections |
Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |
Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |
Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |
Chapter 7- Permutations and Combinations | Chapter 15- Statistics |
Chapter 8- Binomial Theorem | Chapter 16- Probability |
NCERT solutions of class 11 maths
CBSE Class 11-Question paper of maths 2015
CBSE Class 11 – Second unit test of maths 2021 with solutions
Class 11 -Physics
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions
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)}
Ans. In the ordered pair (2, 1),(5,1),(8,1),(11,1),(14,1),(17,1), all the elements 2,5,8,11,14 and 17 has have a unique image,therefore given relationship is a function.
In the set R = {(2, 1),(5,1),(8,1),(11,1),(14,1),(17,1)},the first element of the ordered pair is the domain
Therefore
Domain of the function= {2,5,8,11,14, 17}
In the set R = {(2, 1),(5,1),(8,1),(11,1),(14,1),(17,1)},the second element of the ordered pair is the range
Therefore
Range of the function= {1}
(ii) R={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)}
In the given relation the elements 2,4,6,8,10,12 and 14 have a unique image,therefore given relation is a function
In the set of ordered pair {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)},first element shows the domain of the function
Therefore, domain of the function = {2,4,6,8,10,12,14}
In the set of ordered pair {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)},second element shows the range of the function
Range of the function = {1,2,3,4,5.6,7}
(iii)R={1,3),(1,5),(2,5)}
In the given relation the element 1 has two images 3 and 5, in this relation every element have not a unique image, therefore given relation is not a function
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions
Q2.Find the domain and range of the following real function:
Ans. (i) The given function f(x) is defined for x ∈ R
In the value of , x can have 0, positive and negative value,so it can be expressed as follows
Since the function is defined as , therefore the function can have 0 or negative value, the function can be expressed as follows
In both cases x≥0 and x<0, f(x) have 0 and negative value
Therefore the range of the function is (-∞,0]
Since for x ∈ R, √x ≥ 0
⇒9 – x² ≥ 0
⇒9 ≥ x²
⇒x²≤ 9
The domain is [-3,3]
The given function is f(x) = √(9 -x²)
For any value of x within the domain [-3.3], the minimum and maximum value of f(x) decides the range of f(x)
It can be observed that for x = 0, f(x) = 3 and for x = 3, f(x) = 0
The possibel values of f(x) lies between 0 to 3
Therefore the range of f(x) is [0,3]
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions
Q3. A function f is defined by f(x) = 2x -5. Write down the values of
(i) f(0) (ii) f(7) (iii) f(-3)
Ans. The given function is
f(x) = 2x -5
(i) f(0) = 2×0-5 = -5
(ii) f(7) = 2× 7- 5 = 9
(iii) f(-3) = 2×-3 -5=-11
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions
Q4. The function ‘t’ which maps temperature in degree Celcius into temperature in degree Fahrenheit is defined by
Find (i) t(0) (ii) t(28) (iii) t(-10) (iv) The value of C when t(C) =212
Ans. The given function is
(iv) We are given t(C) =212
C = 100
NCERT solutions for class 11 exercise 2.3 chapter 2 Relations and Functions
Q5.Find the range of each of the following functions
(i) f(x) = 2 -3x , x ∈ R, x > 0
(ii) f(x) = x²+2 , x is a real number
(iii)f(x) = x , x is a real number
Ans.(i) The given function is f(x) = 2 -3x
Also given
x > 0
Multiplying by x in both sides of inequality
3x > 0
⇒2-3x < 2-0
⇒2-3x <2
⇒f(x) <2
It indicates that all possible values of f(x) are less than 2
Therefore range of f(x) is (-∞,2)
(ii) f(x) = x²+2 , x is a real number
We are given that x is a real number
Therefore
x² ≥ 0
Adding 2 both sides
x²+2 ≥ 0+2
⇒x²+2 ≥ 2
⇒f(x) ≥ 2
It indicates that all possible values of f(x) are greater and equal to 2
Therefore range of f(x) is [2,∞)
(iii) The given function is f(x) = x
Also given x is a real number
Since f(x) = x, It indicates that all possible values of f(x) are all real numbers
Therefore range of the function is f(x) =R
NCERT Solutions of class 9 maths
Chapter 1- Number System | Chapter 9-Areas of parallelogram and triangles |
Chapter 2-Polynomial | Chapter 10-Circles |
Chapter 3- Coordinate Geometry | Chapter 11-Construction |
Chapter 4- Linear equations in two variables | Chapter 12-Heron’s Formula |
Chapter 5- Introduction to Euclid’s Geometry | Chapter 13-Surface Areas and Volumes |
Chapter 6-Lines and Angles | Chapter 14-Statistics |
Chapter 7-Triangles | Chapter 15-Probability |
Chapter 8- Quadrilateral |
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NCERT solutions of class 12 maths
Chapter 1-Relations and Functions | Chapter 9-Differential Equations |
Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |
Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |
Chapter 4-Determinants | Chapter 12-Linear Programming |
Chapter 5- Continuity and Differentiability | Chapter 13-Probability |
Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |
Chapter 7- Integrals | |
Chapter 8-Application of Integrals |