# Part - 2 Lecture - 4 Chapter 1 Relations and Functions

“Put your heart, mind, and soul into even your smallest acts. This is the secret of success.” —*Swami Sivananda*

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

**Question 7.** Let A = [-1, 1] Then, discuss whether the following functions defined on A are one-one, onto or bijective:**a.** \( f(x) = \frac{x}{2}\)**b.** \( g(x) = | x | \)**c.** \( h(x) = x| x |\)**d.** \( k(x) = x^2 \)

**Question 8.** Let \( f : N \to N \) be defined by \( f(n)=\begin{cases} {\frac{n + 1}{2}}, & \text{ if n is odd} \\ {\frac{n}{2}}, & \text{ if n is even} \end{cases} \) for all \( n \in N\). State whether the function *f* is bijective. Justify your answer.

**Question 9.** Let A and B be sets. Show that f : A × B → B × A such that f (a, b) = (b, a) is bijective function.