The domain of the function cosec ^-1(1+x/x) is

Question

The domain of the function cosec^-1\(\left(\cfrac{1+x}{x}\right)\) is :

(1) \(\left(-1, -\cfrac{1}{2}\right]\cup(0,\infty)\)

(2) \(\left[-\cfrac{1}{2},0\right)\cup[1,\infty)\)

(3) \(\left(-\cfrac{1}{2},\infty\right)-\{0\}\)

(4) \(\left[-\cfrac{1}{2},\infty\right)-\{0\}\)

Answer 1

Correct answer is:  (4) \(\left[-\cfrac{1}{2},\infty\right)-\{0\}\)