Domain of f(x) = , where {.} denotes the fractional part o…

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Domain of f(x) = , where {.} denotes the fractional part of x, is

(- ∞ ∞ , 0) ∪ ∪ (0, 2]

[1, 0)

(- ∞ ∞ , ∞ ∞ )~ [0, 2)

(- ∞ ∞ , 0) ~ (0, 1] ∪ ∪ [2, ∞ ∞ )

Text Solution

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The correct answer is:

We must have ≥ ≥ 0. We have two cases

(i) x ≥ ≥ 1 and x > 2{x} ⇒ ⇒ x ≥ ≥ 1 and x ≥ ≥ 2.

Common part is [2, ∞ ∞ ).

(ii) x ≤ 1 and x < 2{x} ⇒ ⇒ x < 1 and x ≠ ≠ 0.

Common part is x ∈ ∈ (- ∞ ∞ , 0) ∪ ∪ (0, 1).

Finally x = 1 is also a point of the domain.

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