Question

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

• A. $\left(-1,-\frac{1}{2}\right] \cup(0, \infty)$
• B. $\left[-\frac{1}{2}, 0\right) \cup[1, \infty)$
• C. $\left(-\frac{1}{2}, \infty\right)-\{0\}$
• D. $\left[-\frac{1}{2}, \infty\right)-\{0\}$

Answer 1

Answer: (D)

$\frac{1+x}{x} \in(-\infty,-1] \cup[1, \infty)$
$\frac{1}{x} \in(-\infty,-2] \cup[0, \infty)$
$x \in\left[-\frac{1}{2}, 0\right) \cup(0, \infty)$
$x \in\left[-\frac{1}{2}, \infty\right)-\{0\}$