Find the domain
Question:

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

Solution:

Let $f(x)=g(x)+h(x)$, where $g(x)=\cot x$ and $h(x)=\cot ^{-1} x$

Therefore, the domain of $f(x)$ is given by the intersection of the domain of $g(x)$ and $h(x)$

The domain of $g(x)$ is $\mathrm{R}-\{n \pi, n \dot{E} Z\}$

The domain of $h(x)$ is $(0, \pi)$

Therfore, the intersection of $g(x)$ and $h(x)$ is $\mathrm{R}-\{n \pi, n \dot{E} Z\}$