NCERT solution Class 12 relations and functions

NCERT Solutions

Class 12 Maths

Relations and Functions

NCERT Questions

Ex. 1.1 Q1
Ex. 1.1 Q2
Ex. 1.1 Q3
Ex. 1.1 Q4
Ex. 1.1 Q5
Ex. 1.1 Q6
Ex. 1.1 Q7
Ex. 1.1 Q8
Ex. 1.1 Q9
Ex. 1.1 Q10
Ex. 1.1 Q11
Ex. 1.1 Q12
Ex. 1.1 Q13
Ex. 1.1 Q14
Ex. 1.1 Q15
Ex. 1.1 Q16
Ex. 1.2 Q1
Ex. 1.2 Q2
Ex. 1.2 Q3
Ex. 1.2 Q4
Ex. 1.2 Q5
Ex. 1.2 Q6
Ex. 1.2 Q7
Ex. 1.2 Q8
Ex. 1.2 Q9
Ex. 1.2 Q10
Ex. 1.2 Q11
Ex. 1.2 Q12
Ex. 1.3 Q1
Ex. 1.3 Q2
Ex. 1.3 Q3
Ex. 1.3 Q4
Ex. 1.3 Q5
Ex. 1.3 Q6
Ex. 1.3 Q7
Ex. 1.3 Q8
Ex. 1.3 Q9
Ex. 1.3 Q10
Ex. 1.3 Q11
Ex. 1.3 Q12
Ex. 1.3 Q13
Ex. 1.3 Q14
Ex. 1.4 Q1
Ex. 1.4 Q2
Ex. 1.4 Q3
Ex. 1.4 Q4
Ex. 1.4 Q5
Ex. 1.4 Q6
Ex. 1.4 Q7
Ex. 1.4 Q8
Ex. 1.4 Q9
Ex. 1.4 Q10
Ex. 1.4 Q11
Ex. 1.4 Q12
Ex. 1.4 Q13
Misc. Ex. Q1
Ex. 1.4 Q2
Ex. 1.4 Q3
Misc. Ex. Q4
Misc. Ex. Q5
Misc. Ex. Q6
Misc. Ex. Q7
Misc. Ex. Q8
Misc. Ex. Q9
Misc. Ex. Q10
Misc. Ex. Q11
Misc. Ex. Q12
Misc. Ex. Q13
Misc. Ex. Q14
Misc. Ex. Q15
Misc. Ex. Q16
Misc. Ex. Q17
Misc. Ex. Q18
Misc. Ex. Q19

Misc. Ex. Q1

Let f: R → R be defined as f(x) = 10x + 7. Find the function g: R → R such that

g o f = f o g = I_R.

It is given that f: R → R is defined as f(x) = 10x + 7

For one – one:

Let f(x) = f(y), where x, y ∈ R.

⇒ 10x + 7 = 10y + 7

⇒ x = y

So, f is a one – one function.

For onto:

For y ∈ R, let y = 10x + 7

⇒ x = (y – 7)/10 ∈ R

Therefore, for any y ∈ R, there exists x = (y – 7)/10 ∈ R such that

f(x) = f((y−7)/10) = 10(y−7)/10 + 7 = y − 7 + 7 = y

So, f is onto.

Therefore, f is one – one and onto.

Thus, f is an invertible function.

Let us define g: R → R as g(y) = (y – 7)/10

Now, we have

gof(x) = g(f(x)) = g(10x + 7) = {(10x + 7) – 7}/10 = 10x/10 = x and

fog(y) = f(g(y)) = f ((y – 7)/10) = 10(y – 7)/10 + 7 = y − 7 + 7 = y

So, g o f = I_R and f o g = I_R

Hence, the required function g: R → R is defined as g(y) = (y – 7)/10

Relations and Functions Class 12 Maths NCERT Chapter 1 NCERT Solutions

Solving NCERT textbook questions of Relations and Functions Class 12 Maths NCERT Chapter 1 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 12 Maths Relations and Functions, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 12 Maths Relations and Functions Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Relations and Functions Class 12 Maths Notes.
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By following these steps and actively engaging with the NCERT solutions module of Class 12 Maths Relations and Functions NCERT Chapter 1, you can improve your learning outcomes, develop a better grasp of the subject, and perform well in exams and other academic assessments. Remember that consistent practice, understanding, and application of knowledge are key to academic success.

NCERT solutions of Relations and Functions Class 12 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 12 Maths Relations and Functions NCERT solutions.