Sets, Relations & Functions
Functions
nta_pyq_2025_jan
Grade 11
Question:
Let [x] denote the greatest integer less than or equal to x. Then the domain of f (x) = sec -1 (2[x] + 1) is :
(-\infty, -1] \cup [0, \infty)
(-\infty, -1] \cup [1, \infty)
(-\infty, \infty)
(-\infty, \infty) - {0} 2
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
-1 f (x) = sec (2[x] + 1) (3) \Rightarrow 2[x] + 1 \ge 1 or 2[x] + 1 \le -1 \Rightarrow 2[x] \ge 0 or 2[x] \le -2 \Rightarrow [x] \ge 0 or [x] \le -1 \Rightarrow x \ge 0 or x \le 0 Domain of f (x) is (-\infty, \infty)
Correct Answer: 3