Let A = R – {3} and B = R – | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question:

Let A = R – {3} and B = R – {1}. Consider the function  f : A → B defined by

. Is f one-one and onto? Justify your answer. 

 

Answer:

A = R - {3}, B = R - {1}

f: A → B is defined as.

.

∴ f is one-one.

Let y ∈B = R - {1}. Then, y ≠ 1.

The function f is onto if there exists x ∈A such that f(x) = y.

Now,

Thus, for any y ∈ B, there existssuch that

Hence, function f is one-one and onto.


Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

  • Read the question carefully and focus on the core concept being asked.
  • Reference examples and data from the chapter when answering questions about Relations and Functions.
  • Review previous year question papers to get an idea of how such questions may be framed in exams.
  • Practice answering questions within the time limit to improve your speed and accuracy.
  • Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Comment(s) on this Question

Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 10: Let A = R – {3} and B = R – {1}. Consider the function  f : A → B defined by ....