Let [x] denote the greatest integer less than or equal to x.

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:

Accepted Answer

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

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