If $f(x) +2y \bigg(\large\frac{1}{x}\bigg)$$=3x,x \neq 0$ and $S=\{x \in R:f(x)=f(-x)\}$ then S:

Question

$\begin{array}{1 1} \text{(1) is an empty set} \\ \text{(2) contains exactly one element} \\ \text{(3) contains exactly two elements} \\ \text{(4) contains more than two elements} \end{array}$