Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Domain of f(x) = 
; where [.] denotes the greatest integer function, is
A
(- ∞ ∞ , -2) ∪ ∪ [1, ∞ ∞ )
B
(- ∞ ∞ , - 
) ∪ ∪ [1, ∞ ∞ )
) ∪ ∪ [1, ∞ ∞ )
C
(- ∞ ∞ , -3) ∪ ∪ [1, ∞ ∞ )
D
( − − ∞ ∞ , 
) ∪ ∪ [1, ∞ ∞ )
) ∪ ∪ [1, ∞ ∞ )
Text Solution
Verified by ExpertsThe correct answer is:
D
We must have [x] − − 1 + x 2 ≥ ≥ 0
⇒ ⇒ x 2 - 1 ≥ ≥ -[x]
The graphs of y = x 2 - 1 and y = − − [x] intersect somewhere in (-2, -1). Thus at the point of intersection x 2 – 1 = 2 ⇒ ⇒ x = √ √ 3
From the adjacent graph we get domain as
(- ∞ ∞ , 
] ∪ ∪ [1, ∞ ∞ )
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