Question

Find the domain of $f\left(x\right)=\cot x+{\cot }^{-1}x$.

Answer 1

$\cot x$ is defined for $x\in R-\{n\pi ,n\in Z\}$
and ${\cot }^{-1}x$ is defined for $x\in R$.

Now we take the intersection of both domains

$\therefore$ domain for $f\left(x\right)$ is $R-\{n\pi ,\in Z\}$.