JEE MAIN - Mathematics (2021 - 26th August Evening Shift - No. 6)
The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :
$$\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )$$
$$\left[ { - {1 \over 2},0} \right) \cup [1,\infty )$$
$$\left( { - {1 \over 2},\infty } \right) - \{ 0\} $$
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\} $$
Explanation
$${{1 + x} \over x} \in ( - \infty , - 1] \cup [1,\infty )$$
$${1 \over x} \in ( - \infty , - 2] \cup [0,\infty )$$
$$x \in \left[ { - {1 \over 2},0} \right) \cup (0,\infty )$$
$$x \in \left[ { - {1 \over 2},0} \right) \cup \{ 0\} $$
$${1 \over x} \in ( - \infty , - 2] \cup [0,\infty )$$
$$x \in \left[ { - {1 \over 2},0} \right) \cup (0,\infty )$$
$$x \in \left[ { - {1 \over 2},0} \right) \cup \{ 0\} $$
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