1) The domain of the function $f(x)= \frac{1}{\sqrt{[x]^{2}-[x]^{}-2}}$ is Here [x] denotes the greatest integer not exceeding the value of [x] A) $(-\infty,-2)\cup (1, \infty)$ B) $(-\infty,-2)\cup (0, \infty)$ C) $(-\infty,-2)\cup (2, \infty)$ D) $(-\infty,-1)\cup (3, \infty)$ Answer: Option DExplanation:We have, $f(x)= \frac{1}{\sqrt{[x]^{2}-[x]^{}-2}}$ f(x0 is defined when $[x]^{2}-[x]-2 >0$ $([x]-2)([x]+1)>0$ [x] >2 and [x] <-1 $x\geq 3 $and x<-1 $\therefore$ Domain of f(x) is x $\in $$(-\infty,-1)\cup (3, \infty)$
