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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 $x \neq = 2$ .

If $n$ is a nonnegative integer, solve $[(x - 1) / (2 - x)] = n$ .

Options:

Answer:

Solution:

The floor equation means $n \leq (x - 1) / (2 - x) < n + 1$ . For $n \geq 0$ the solution has $x < 2$ ; solving gives $(2 n + 1) / (n + 1) \leq x < (2 n + 3) / (n + 2)$ .

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

⏱ 2mℹ️ Source: QB

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