Solve this:


Q. Let f be a real valued function defined by 

$\mathrm{f}\left(\mathrm{x}\right)=\frac{\left[\left(\mathrm{x}-1\right)\left(\mathrm{x}-2\right)\right]\mathrm{In}\left(\left[\left(\mathrm{x}-1\right)\left(\mathrm{x}-2\right)\right]\right)}{\sqrt{-\left(\mathrm{x}+3\right)\left(\mathrm{x}-4\right)}}$
Where[.] denotes the greatest integer function, then domain of the function is.

$$\begin{gathered} \left(\mathrm{A}\right) \left(-2,\frac{3-\sqrt{5}}{2}\right)\cup \left(\frac{3+\sqrt{5}}{2},4\right) \\ \left(\mathrm{B}\right) (-3,\frac{3-\sqrt{5}}{2}] \cup [\frac{3+\sqrt{5}}{2},3) \\ \left(\mathrm{C}\right) (-3,\frac{3-\sqrt{5}}{2}] \cup [\frac{3+\sqrt{5}}{2},4) \\ \left(\mathrm{D}\right) (-3,\frac{3+\sqrt{5}}{2}]\cup [\frac{3+\sqrt{5}}{2},4) \end{gathered}$$