The domain of the function [ cosec ^ - 1( 1 + x x )] is :

Question

The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :

Accepted Answer

$${{1 + x} \over x} \in ( - \infty , - 1] \cup [1,\infty )$$

$${1 \over x} \in ( - \infty , - 2] \cup [0,\infty )$$

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

$$x \in \left[ { - {1 \over 2},0} \right) \cup \{ 0\} $$

Solutions · 1