Match the following column – I is representing function and column – II is representing range of the function (where [.] denotes greatest integer function and {.} denotes fractional part function)

	Column-I		Column-II
P	$f_1\left(x\right)=\left[{\text{log}}_{\sqrt{2}}\sqrt{{(x-1)}^3|+|{(x-3)}^3\mid }\right]$	1	set of all non-positive integers $\cup \left\{1\right\}$
Q	$f_2\left(x\right)=[{\text{log}}_{\sqrt{2}}(\text{sin}\left(\text{ln}\left(\frac{\sqrt{4-x^2}}{1-x}\right)\right)+\text{cos}\left(\text{ln}\left(\frac{\sqrt{4-x^2}}{1-x}\right)\right)]$	2	set of all non negative integers
R	$f_3\left(x\right)=\left\{\frac{|x+5|-2}{x^2+10x+21}\right\}$	3	set of all positive integers
S	$f_4\left(x\right)=\left[\frac{1}{\sqrt{\text{ln}\left({\text{cos}}^{-1}x\right)}}\right]$	4	$(0,\frac{1}{2}]-\left\{\frac{1}{4}\right\}$