Question

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

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