Sets, Relations & Functions
Domain of Floor-Based Function
nta_pyq_2023_apr
Grade 11
Question:
The domain of $f(x)=\dfrac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where $[x]$ denotes the greatest integer $\leq x$)
$(-\infty,-3]\cup(5,\infty)$
$(-\infty,-2)\cup[6,\infty)$
$(-\infty,-2)\cup(5,\infty)$
$(-\infty,-3]\cup[6,\infty)$
Step-by-Step Solution
Key Concept: Need $[x]^2-3[x]-10>0\Rightarrow([x]-5)([x]+2)>0\Rightarrow[x]<-2$ or $[x]>5$.
Domain $=(-\infty,-2)\cup[6,\infty)$.
Correct Answer: 2