Question

The domain of the function $f\left(x\right)=\frac{1}{[x{]}^2-7[x]+10}$ is
(where $[.]$ denotes the greatest integer function)

Answer 1

$f\left(x\right)=\frac{1}{[x{]}^2-7[x]+10}$
For function to be defined,
$[x{]}^2-7[x]+10\ne 0\Rightarrow (\left[x\right]-5\left)\right(\left[x\right]-2)\ne 0\Rightarrow [x]\ne 2,5\Rightarrow x\notin [2,3)\text{and}x\notin [5,6)$

$\therefore$ Domain of $f\left(x\right)=R-[2,3)\cup [5,6)$