Verified Solution • 2025–26 Session moderate

QJEEM25Maac0f: JEE Main 2025 Mathematics - Class 12 JEEM25Maac0f Solution: Let [x] denote the greatest integer less than or equal to x.…

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x)=sec⁡−1(2[x]+1)f(x) = \sec^{-1}(2[x] + 1) is:

Multiple Choice Options

  • A (−∞,∞)(-\infty, \infty)
  • B (−∞,∞)−{0}(-\infty, \infty)- \{0\}
  • C (−∞,−1]∪[0,∞)(-\infty, -1] \cup [0, \infty)
  • D (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)

Step-by-Step Verified Solution

amp;2[x]+1≤−1 or 2[x]+1≥1amp;⇒[x]≤−1∪[x]≥0amp;⇒x∈(−∞,0)∪x∈[0,∞)amp;⇒x∈(−∞,∞)\begin{aligned}& 2[\mathrm{x}]+1 \leq-1 \text { or } 2[\mathrm{x}]+1 \geq 1 \\& \Rightarrow[\mathrm{x}] \leq-1 \cup[\mathrm{x}] \geq 0 \\& \Rightarrow \mathrm{x} \in(-\infty, 0) \cup \mathrm{x} \in[0, \infty) \\& \Rightarrow \mathrm{x} \in(-\infty, \infty)\end{aligned}

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