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

*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.