Question

The domain of the function $f\left(x\right)=\sin \left(\frac{1}{x}\right)$ is

• A. $x\in R$
• B. $x\in R-\left\{0\right\}$
• C. $x\in (-1,1)$
• D. $x\in [-1,1]$

Answer 1

The correct option is B $x\in R-\left\{0\right\}$

$f\left(x\right)=\sin \frac{1}{x}$

Domain of $\sin \left(x\right)$ is $x\in R\Rightarrow \frac{1}{x}\in R$

$\because atx=0$

$\left(\frac{1}{x}\right)becomes\infty$

$\therefore domainoff\left(x\right)=x\in R-\left\{0\right\}$

$\therefore$ The option is $B$