The function f is defined by ~$f\left ( x \right )=-\frac{1}{x}$~ for all nonzero numbers x.  If ~$f\left ( a \right )=-\frac{1}{2}$~ and ~$f\left ( ab \right )=\frac{1}{6}$~, then b =

3

~$\frac{1}{3}$~

~$-\frac{1}{3}$~

-3

-12