Domain of f(x) = sin − − 1 , where [.] and {.} denote the …

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published on: August 13, 2026

Domain of f(x) = sin − − 1 , where [.] and {.} denote the greatest integer function and fractional part respectively, is

(0, 1)

(-1, 1) ~ {0}

(-2, 2) ~ {-1, 0, 1}

None of these

Text Solution

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The correct answer is:

We must have, − − 1 ≤ ≤ 1

From − − 1 ≤ , we get ≥ ≥ 0

⇒ ⇒ > 0 ⇒ ⇒ x ∈ ∈ (0, ∞ ∞ ) ~ I + .

From, ≤ 1 we get, ≤ 0

⇒ ⇒ [x] ≤ {0} ⇒ ⇒ x ∈ ∈ (- ∞ ∞ , 0) ∪ ∪ (0, 1)~I + Thus domain is (0, 1).

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