Question

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

Answer 1

Let f(x) = g(x) + h(x), where $g\left(x\right)=\cot x\mathrm{and}h\left(x\right)={\cot }^{-1}x$
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 R − { nπ, n ⋵ Z}
The domain of h(x) is (0, π )
Therfore, the intersection of g(x) and h(x) is R − { nπ, n ⋵ Z}