Question

Find the domain of `f(x)=cotx+cot^-1x`

Answer 1

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

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}