We can enumerate the sequence to find the coefficients,
i.e. {3+2(0),3+2(1),3+2(2),...} = {3,5,7,9,11...}
Now we can form the equation as:
f(x) = $3x^{0}+5x^{1}+7x^{2}+9x^{3}+...$ --> 1
Now we can take $xf\left ( x \right )$
ie. $xf\left ( x \right ) = 3x^{1}+5x^{2}+7x^{3}+...$ ---> 2
Now subtracting first equation from second we get,
$(1-x)f\left ( x \right ) = 3x^{0}+2x^{1}+2x^{2}+2x^{3}...$
Solve for f(x) we get option D.