Question

The domain of the function $f\left(x\right)=\frac{\sin \left(\log \right(x^2-4x+4\left)\right)}{\left(\right[x]-1)}$, where $[.]$ denotes the greatest integer function, is

• A. $R-[2,\infty )$
• B. $(0,\infty )$
• C. $R-[1,\infty )$
• D. $R-[1,2]$

Answer 1

The correct option is D $R-[1,2]$

$f\left(x\right)=\frac{\sin \left(\log \right(x^2-4x+4\left)\right)}{\left[x\right]-1}$

$\left[x\right]-1\ne 0$
$\Rightarrow \left[x\right]\ne 1\Rightarrow x\notin [1,2)$

$x^2-4x+4>0$
$\Rightarrow (x-2{)}^2>0$
$\Rightarrow x-2\ne 0\Rightarrow x\ne 2$

Therefore, domain of $f$ is $R-[1,2]$