# 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

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.