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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let $f (x) = sin^{- 1} ([(x - 1) / (2 - x)])$ , where $⌊ \cdot ⌋$ denotes the floor function and $x \neq = 2$ .

What is the domain of f?

Options:

Answer:

Solution:

The floor must belong to ${- 1, 0, 1}$ . Thus $- 1 \leq (x - 1) / (2 - x) < 2$ . Solving these inequalities together gives $x < 5/3$ , with all smaller real x admitted.

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: QB

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