Match the statements of Column – I with values of Column – II : 

	Column – I		Column – II
A)	If $f\left(x\right)=\left\{\begin{array}{ccc}x+1,& when& x<0\\ x^2-1,& when& x\ge 0\end{array}\right.,$  then    fof(x) for $-1\le x<0$   is	P)	$\frac{x-3}{2}$
B)	If    $f\left(\frac{2\tan x}{1+{\tan }^{2}x}\right)=\frac{\left(\cos 2x+1\right)\left({\sec }^{2}x+2\tan x\right)}{2}$ Then f(x) is	Q)	$x^2+2x$
C)	If $f\left(x+y+1\right)={\left(\sqrt{f\left(x\right)}+\sqrt{f\left(y\right)}\right)}^2$  for all x, y  $\in$ R  and f(0) = 1, then f(x) is	R)	1 + x
D)	If 4 < x < 5 and $f\left(x\right)=\left[\frac{x}{4}\right]+2x+2$, where [y]    Is the greatest integer  $\le$ y, then $f^{-1}\left(x\right)$  is	S)	${\left(x+1\right)}^2$

The correct match :