The function f(x)= is discontinuous on the set: - Vidyadip

MCQ

The function $\text{f(x)}=\tan\text{x}$ is discontinuous on the set:

A
$\{\text{n}\pi:\text{n}\in\text{z}\}$
B
$\{2\text{n}\pi:\text{n}\in\text{z}\}$
✓
$\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$
D
$\Big\{\frac{\text{n}\pi}{2}:\text{n}\in\text{z}\Big\}$

✓

Answer

Correct option: C.

$\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$

When $\tan(2\text{n}+1)\frac{\pi}{2}=\tan\Big(\text{n}\pi+\frac{\pi}{2}\Big)=-\cot\text{n}\pi,$ it is not defined at the integral points.
$[\text{n}\in\text{z}]$

Hence, f(x) is discontinuous on the set $\{(2\text{n}+1)\frac{\pi}{2}:\text{n}\in\text{z}\}$

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