First slide

Functions (XII)

Question

The period of the function $f (x)$ $= {\begin{matrix} 1, when x is a rational \\ 0, when x is an irrational \end{matrix}$ is:

Moderate

A

1
B

2
C

Non-periodic
D

none of these

Solution

For every rational number T, we have
$f (T + x)$ $= {\begin{matrix} 1, when x is a rational \\ 0, when x is an irrational \end{matrix}$

But there is no least positive value of T for which $f (T + x) = f (x)$ because there are infinite number of rational numbers between any two rational numbers.

Therefore, $f (x)$ is a periodic function having no fundamental period.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App