Question

Domain of f(x) = $\sqrt{\lbrack x\rbrack - 1 + x^{2}}$; where [.] denotes the greatest integer function, is

• A. (-∞, -2) ∪ [1, ∞)
• B. (-∞, - $\sqrt { 2 }$ ) ∪ [1, ∞)
• C. (-∞, -3) ∪ [1, ∞)
• D. (−∞, $- \sqrt { 3 }$) ∪ [1, ∞)

Answer 1

Answer: (D)

(−∞, $- \sqrt { 3 }$) ∪ [1, ∞)

Answer 2

We must have [x] − 1 + x² ≥ 0

⇒ x² - 1 ≥ -[x]

The graphs of y = x² - 1 and y = −[x] intersect somewhere in (-2, -1). Thus at the point of intersection x² – 1 = 2 ⇒ x = √3

From the adjacent graph we get domain as

(-∞, $- \sqrt { 3 }$ ] ∪ [1, ∞)