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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Aicharya · Accepted Answer

$\begin{array}{ll}
f(x)=\sec ^{-1}(2[x]+1) \\ \Rightarrow 2[x]+1 \geq 1 & \text { or } 2[x]+1 \leq-1 \\ \Rightarrow 2[x] \geq 0 & \text { or } 2[x] \leq-2 \\ \Rightarrow[x] \geq 0 & \text { or }[x] \leq-1 \\ \Rightarrow x \geq 0 & \text { or } x \leq 0
\end{array}$
Domain of $f(x)$ is $(-\infty, \infty)$

Let $[x]$ denote the greatest integer less than or equal to $x$. Then the domain of $f(x)=\sec…

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