AP EAMCET · Maths · Functions
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.
- A \(R-(-1,3]\)
- B \(R-[-1,3)\)
- C \(R-(-1,3)\)
- D \(R-[-1,3]\)
Answer & Solution
Correct Answer
(A) \(R-(-1,3]\)
Step-by-step Solution
Detailed explanation
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 \(\begin{aligned} & {[x]^2-[x]-2 > 0} \\ & \Rightarrow \quad\{[x]-2\}\{[x]+1\} > 0 \\ & {[x] \in \mathbf{R}-(-1,2)} \\ \end{aligned}\) So,…
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