If  $f:R^{+}\to R$ be an increasing function such that $xf\left(x\right)+2>0$  and  $f\left(x\right).f\left(\frac{xf\left(x\right)+4}{x}\right)=1$ then match the following

Column – I		Column – II
A)	The value of $[1-f\left(1\right)]$  ([.] GIF)	P)	0
B)	The value of  $\left|\left[f\left(\frac{1}{2}\right)\right]\right|$ equals ([.] GIF)	Q)	1
C)	The value of $[f\text{'}\left(1\right)]$  is ([.] GIF)	R)	2
D)	Number of solutions of  $\sin x-f\left(8\right)=0$ in $[-\pi ,2\pi ]$  is	S)	3
		T)	4