Verified Solution • 2025–26 Session moderate

QJEEM21Ma6b06: JEE Main 2021 Mathematics - Class 12 JEEM21Ma6b06 Solution: The domain of the function is :

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

Multiple Choice Options

  • A (−1,−12]∪(0,∞)\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )
  • B [−12,0)∪[1,∞)\left[ { - {1 \over 2},0} \right) \cup [1,\infty )
  • C (−12,∞)−{0}\left( { - {1 \over 2},\infty } \right) - \{ 0\}
  • D [−12,∞)−{0}\left[ { - {1 \over 2},\infty } \right) - \{ 0\}

Step-by-Step Verified Solution

1+xx∈(−∞,−1]∪[1,∞){{1 + x} \over x} \in ( - \infty , - 1] \cup [1,\infty )

1x∈(−∞,−2]∪[0,∞){1 \over x} \in ( - \infty , - 2] \cup [0,\infty )

x∈[−12,0)∪(0,∞)x \in \left[ { - {1 \over 2},0} \right) \cup (0,\infty )

x∈[−12,0)∪{0}x \in \left[ { - {1 \over 2},0} \right) \cup \{ 0\}

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