Let $[x]$ denote the greatest integer less than or equal to $x$. Then the domain of $f(x)=\sec ^{-1}(2[x]+1)$ is : [JEE Main 2025, 28 Jan (Shift 2)]

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YESPYQ · Accepted Answer

Correct answer: a) $(-\infty ,\infty )$. Domain of ${\text{sec}}^{-1}x$ is $\mathrm{x}\in (-\infty ,-1]\cup [1,\infty )$ $2[x]+1 \leq-1$ or $2[x]+1 \geq 1$ $\Rightarrow[x] \leq-1$ or $[x] \geq 0$ $\Rightarrow \mathrm{x} \in(-\infty, 0)$ or $x \in[0, \infty)$ $\Rightarrow x \in(-\infty, \infty)$

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

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