##### Tallentex 2025 - ALLEN's Talent Encouragement Exam

ApplyRegister for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Edited By Vishal kumar | Updated on Nov 15, 2023 10:08 AM IST

**NCERT Solutions for Class 11 Maths Chapter 2: Relations and Functions Miscellaneous Exercise- **In the previous exercises of this chapter NCERT Solutions For Class 11 Maths Chapter 2 Relations and Functions, you have learned about the relations, domain, codomain, and range of the relations, functions, domain and range of the functions, different types of function and their graphs, etc. In the NCERT solutions for Class 11 Maths chapter 2 miscellaneous exercise, you will get questions related to relations, functions, domain and range of relations and functions, etc. As the name suggests the miscellaneous exercise consists of mixed kinds of questions from all the topics of this miscellaneous exercise class 11 chapter 2.

**JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | **

**Suggested: ****JEE Main: high scoring chapters | ****Past 10 year's papers**

This Story also Contains

- NCERT Solutions for Class 11 Maths Chapter 2 - Relations and Functions Miscellaneous Exercise- Download Free PDF
- NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions Miscellaneous Exercise
- Relations And Functions Class 11 Chapter 2 Miscellaneous Exercise
- More About NCERT Solutions for Class 11 Maths Chapter 2 Miscellaneous Exercise:-
- Benefits of NCERT Solutions for Class 11 Maths Chapter 2 Miscellaneous Exercise:-
- Key Features of NCERT Class 11 Maths Ch 2 Miscellaneous Exercise Solutions
- NCERT Solutions of Class 11 Subject Wise
- Subject Wise NCERT Exampler Solutions

If you solved all the previous exercises of this chapter, you can solve all the NCERT problems of class 11 chapter 2 maths miscellaneous solutions by yourself. The miscellaneous exercise Chapter 2 Class 11 is considered to be tougher as compared to the previous exercises of this chapter. So it is not easy to solve these problems on your own at first, but Class 11 Maths chapter 2 miscellaneous exercise solutions are here to help you. You will find all the NCERT problems solved in a descriptive manner. You can NCERT Solutions if you are looking for NCERT solutions for other classes as well.

**Also, see**

- Relations and Functions Exercise 2.1
- Relations and Functions Exercise 2.2
- Relations and Functions Exercise 2.3

Answer:

It is given that

Now,

And

At x = 3,

Also, at x = 3,

We can see that for , f(x) has unique images.

Therefore, By definition of a function, the given relation is function.

Now,

It is given that

Now,

And

At x = 2,

Also, at x = 2,

We can clearly see that element 2 of the domain of relation g(x) corresponds to two different images i.e. 4 and 6. Thus, f(x) does not have unique images

Therefore, by definition of a function, the given relation is not a function

Hence proved

Question:3 Find the domain of the function

Answer:

Given function is

Now, we will simplify it into

Now, we can clearly see that

Therefore, the Domain of f(x) is

Question:4 Find the domain and the range of the real function f defined by

Answer:

Given function is

We can clearly see that f(x) is only defined for the values of x ,

Therefore,

The domain of the function is

Now, as

take square root on both sides

Therefore,

Range of function is

Question:5 Find the domain and the range of the real function f defined by

Answer:

Given function is

As the given function is defined of all real number

The domain of the function is R

Now, as we know that the mod function always gives only positive values

Therefore,

Range of function is all non-negative real numbers i.e.

Question:6 Let R be a function from R into R. Determine the range of f.

Answer:

Given function is

Range of any function is the set of values obtained after the mapping is done in the domain of the function. So every value of the codomain that is being mapped is Range of the function.

Let's take

Now, 1 - y should be greater than zero and y should be greater than and equal to zero for x to exist because other than those values the x will be imaginary

Thus,

Therefore,

Range of given function is

Question:7 Let f, g : R R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g

Answer:

It is given that

Now,

Therefore,

Now,

Therefore,

Now,

Therefore, values of are respectively

Answer:

It is given that

And

Now,

At x = 1 ,

Similarly,

At ,

Now, put this value of b in equation (i)

we will get,

Therefore, values of a and b are 2 and -1 respectively

Question:9 (i) Let R be a relation from N to N defined by . Are the following true?

for all

Answer:

It is given that

And

for all

Now, it can be seen that But,

Therefore, this statement is FALSE

Question:9 (ii) Let R be a relation from N to N defined by . Are the following true?

implies (b,a) R

Answer:

It is given that

And

implies

Now , it can be seen that and , But

Therefore,

Therefore, given statement is FALSE

Question:9 (iii) Let R be a relation from N to N defined by . Are the following true?

(a,b) R, (b,c) R implies (a,c) R.

Answer:

It is given that

And

implies

Now, it can be seen that because and , But

Therefore,

Therefore, the given statement is FALSE

Answer:

It is given that

and

Now,

Now, a relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B

And we can see that f is a subset of

Hence f is a relation from A to B

Therefore, given statement is TRUE

Answer:

It is given that

and

Now,

As we can observe that same first element i.e. 2 corresponds to two different images that is 9 and 11.

Hence f is not a function from A to B

Therefore, given statement is FALSE

Question:11 Let f be the subset of defined by . Is f a function from Z to Z? Justify your answer.

Answer:

It is given that

Now, we know that relation f from a set A to a set B is said to be a function only if every element of set A has a unique image in set B

Now, for value 2, 6, -2, -6

Now, we can observe that same first element i.e. 12 corresponds to two different images that are 8 and -8.

Thus, f is not a function

Answer:

It is given that

A = {9,10,11,12,13}*And f : A*

Now,

Prime factor of 9 = 3

Prime factor of 10 = 2,5

Prime factor of 11 = 11

Prime factor of 12 = 2,3

Prime factor of 13 = 13

f(n) = the highest prime factor of n.

Hence,

f(9) = the highest prime factor of 9 = 3

f(10) = the highest prime factor of 10 = 5

f(11) = the highest prime factor of 11 = 11

f(12) = the highest prime factor of 12 = 3

f(13) = the highest prime factor of 13 = 13

As the range of f is the set of all f(n), where

Therefore, the range of f is: {3, 5, 11, 13}.

Class 11 Maths chapter 2 miscellaneous solutions consists of questions related to relations, functions, finding the domain and range of the functions, etc. There are five examples related to functions and their properties are given before the miscellaneous exercise chapter 2 Class 11. You can go through these examples in order to get conceptual clarity. The topics covered in this exercise are same as the previous exercises of this chapter, so you can solve the problems of this exercise after solving the previous exercises.

**Also Read| **Relations And Functions Class 11th Notes

- Class 11 Maths chapter 2 miscellaneous exercise solutions are designed by subject matter experts who have expertise in the subject, so you can easily rely upon these solutions.
- NCERT solutions for Class 11 Maths chapter 2 miscellaneous exercise are useful to understand the algebra of functions which is an important concept of function.
- Class 11 Maths chapter 2 miscellaneous solutions are not only important for the CBSE exams but are very useful for competitive exams like JEE Main, SRMJEE, etc.

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook**Comprehensive Clarification:** Miscellaneous exercise class 11 chapter 2 Solutions provide a thorough explanation of all topics, fostering a strong grasp of relations and functions.

**Stepwise Clarity:** These class 11 chapter 2 maths miscellaneous solutions break down each problem, aiding students in following a logical progression of concepts, and ensuring a smoother understanding.

**Clear Conciseness:** Presented in clear and concise language, the class 11 maths miscellaneous exercise chapter 2 solutions simplify complex mathematical concepts, enhancing accessibility for students.

**Free PDF Access:** Additionally, these class 11 chapter 2 miscellaneous exercise solutions offer the convenience of free PDF access, promoting widespread availability and ease of use for all students.

**Also see-**

Happy learning!!!

1. Let f(x) = 2x + 3 than f(3) ?

f(x) = 2x + 3

f(3) = 2(3) + 3 = 6 +3 = 9

2. Let f(x) = 2^x + x + 1 find f(2) ?

f(x) = 2^x + x + 1

f(2) = 2^2 + 2 + 1

f(2) = 4 + 2 + 1 = 7

3. Let f(x) = x^2 and g(x) = x + 2 be two real functions. Find (f+g)(x) ?

f(x) = x^2 and g(x) = x + 2

(f+g)(x) = x^2 + x + 2

4. Let f(x) = x^2 and g(x) = x + 2 be two real functions. Find (f-g)(x) ?

f(x) = x^2 and g(x) = x + 2

(f-g)(x) = x^2 - x - 2

5. Let f(x) = x^2 and g(x) = x + 2 be two real functions. Find (fg)(x) ?

f(x) = x^2 and g(x) = x + 2

(fg)(x) = (x^2)( x + 2)

(fg)(x) = x^3 + 2x^2

6. Let f(x) = x^2 and g(x) = x + 2 be two real functions. Find (f/g)(x) ?

f(x) = x^2 and g(x) = x + 2

(f/g)(x) = (x^2)/( x + 2) where x can't be equal to -2.

Sep 06, 2024

Get answers from students and experts

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top