Question

The domain of $f\left(x\right)=\cot \frac{x}{3}$ is

• A. $(-\infty ,\infty )$
• B. $R-\{n\pi :n\in Z\}$
• C. $R-\{3n\pi :n\in Z\}$
• D. $(0,\infty )$

Answer 1

The correct option is C $R-\{3n\pi :n\in Z\}$

$\cot \frac{x}{3}$ is not defined at
$\frac{x}{3}=n\pi$ for $n\in Z$
$\Rightarrow x=3n\pi$
$\therefore$ domain of $f$ is R $-\{3n\pi :n\in Z\}.$