Medium MCQ +4 / -1 PYQ · JEE Mains 2025

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

  1. A <p>$(-\infty, \infty)$</p> Correct answer
  2. B <p>$(-\infty, \infty)- \{0\}$</p>
  3. C <p>$(-\infty, -1] \cup [0, \infty)$</p>
  4. D <p>$(-\infty, -1] \cup [1, \infty)$</p>

Solution

<p>$$\begin{aligned} & 2[\mathrm{x}]+1 \leq-1 \text { or } 2[\mathrm{x}]+1 \geq 1 \\ & \Rightarrow[\mathrm{x}] \leq-1 \cup[\mathrm{x}] \geq 0 \\ & \Rightarrow \mathrm{x} \in(-\infty, 0) \cup \mathrm{x} \in[0, \infty) \\ & \Rightarrow \mathrm{x} \in(-\infty, \infty) \end{aligned}$$</p>

About this question

Subject: Mathematics · Chapter: Inverse Trigonometric Functions · Topic: Domain and Range

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