Ques. 1JEE Main 2025, 28 January (Evening Shift)
Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = -1(2[x] + 1) is:
- (- , )
- (- , ) - \0\
- (- , -1] [0, )
- (- , -1] [1, )
Answer
(1) (- , )
Solution
-1t is defined for |t| 1, i.e. t -1 or t 1.
2[x] + 1 1 [x] 0 x 0
2[x] + 1 -1 [x] -1 x < 0
Domain = (- , 0) [0, ) = (- , )
(Indeed, 2[x] + 1 is always an odd integer, so |2[x] + 1| 1 for every real x.)
Answer: (1)