# 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 $$f(x) = \frac{x}{x^2 + 1}, \forall x \in R$$