Mathematics - Functions Question with Solution | TestHub

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