Part - 1 Lecture - 4 Chapter 1 Relations and Functions

“In the end, it’s not the years in your life that count. It’s the life in your years.” —Abraham Lincoln

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

Question 1. If \( f : R \to A \), given by \( f(x) = x^2 – 2x + 2 \) is onto functions, find set A.

Question 2. Is \( f : R \to R \), given by f(x) = | x -1 | one – one? Give reason.

Question 3. \( f : R \to B \), given by f(x) = sin x is onto function, then write the set B.

Question 4. Let A = R – {3} and B = R – {1}. Consider the function \( f : A \to B \) defined by \( f(x) = \left ( \frac{x-2}{x-3} \right) \). Is f one-one and onto? Justify your answer.

Question 5. Check the following functions for one-one and onto:
a. \( f : R \to R, f(x) = \frac{2x – 3}{7} \)
b. \( f : R \to R, f(x) = | x + 1 | \)
c. \( f : R – {2} \to R, f(x) = \frac{3x – 1}{x – 2} \)

Question 6. Show that the function \( f : R \to R \) defined by \( f(x) = \frac{x}{x^2 + 1}, \forall x \in R \)