The domain of the function cosec - 1 1 + x x is :

Domain of cos e c - 1 x is x ≤ - 1 o r x ≥ 1 1 + x x ≤ - 1 or 1 + x x ≥ 1 1 + x + x x ≤ 0 or 1 + x - x x ≥ 0 2 x + 1 x ≤ 0 or 1 x ≥ 0 x ∈ - 1 2 , 0 or x ∈ ( 0 , ∞ ) x ∈ - 1 2 , ∞ - { 0 }

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MathematicsFunctionsDomain-RangeEasy2 minPYQ_2021

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

Question diagram: The domain of the function cosec - 1 1 + x x is :

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Answer:

Solution:

Domain of $\cos e c^{- 1} x$ is $x \leq - 1 o r x \geq 1$

$\frac{1 + x}{x} \leq - 1$ or $\frac{1 + x}{x} \geq 1$

$\frac{1 + x + x}{x} \leq 0$ or $\frac{1 + x - x}{x} \geq 0$

$\frac{2 x + 1}{x} \leq 0$ or $\frac{1}{x} \geq 0$

$x \in [\frac{- 1}{2}, 0)$ or $x \in (0, \infty)$

$x \in [- \frac{1}{2}, \infty) - {0}$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: PYQ_2021

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