Let$f:R^{+}\to R$   be an strictly increasing function, such  that $x\text{\hspace{0.17em}f}\left(x\right)+\text{2}>0$  and $f\left(x\right)·f\left(\frac{xf\left(x\right)+4}{x}\right)=1$

	LIST -1		LIST -2
A)	The value of $\left[f^{\text{'}}\left(1\right)\right]$  is : ([.] denotes G.I.F)	P)	2
B)	Number of point(s) of inflection of f(x) is	Q)	1
C)	The value of [1-f(1)] is: [.] denotes G.I.F)	R)	0
D)	Number of solution(s) of sinx-f(8) = 0 in interval $\left[-\mathrm{\pi },2\mathrm{\pi }\right]$  is	S)	4