Find the domain of the real valued function $f(x)=\left([x]^2-[x]-2\right)^{-1 / 2}$, where $[\cdot]$ is the greatest integer function.

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Aicharya · Accepted Answer

Let $y=f(x)=\left([x]^2-[x]-2\right)^{-1 / 2}$ $\Rightarrow \quad y^2=\frac{1}{\sqrt{[x]^2-[x]-2}}$ For real valued $\begin{aligned} & {x^2-x-2 > 0} \ & \Rightarrow \quad{(x-2)(x+1) > 0} \ & {x \in \mathbb{R}-(-1,2)} \ \end{aligned}$ So, $x \in \mathbb{R}-(-1,3]$

Find the domain of the real valued function \(f(x)=\left([x]^2-[x]-2\right)^{-1 / 2}\), where \([\cdot]\) is…

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