Question

Domain of f(x) = $\sqrt{\frac{x - 1}{x - 2\{ x\}}}$, where {.} denotes the

fractional part of x, is

• A. (-∞, 0) ∪ (0, 2]
• B. [1, 0)
• C. (-∞, ∞)~ [0, 2)
• D. (-∞, 0) ~ (0, 1] ∪ [2, ∞)

Answer 1

Answer: (D)

(-∞, 0) ~ (0, 1] ∪ [2, ∞)

Answer 2

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.