Let
$\displaystyle {f{{\left({x}\right)}}}=$ $\displaystyle \frac{{1}}{{6}}{x}+{7}$ $\displaystyle ,\quad-{4}\le{x}\le-{1}$

Determine the domain of $\displaystyle {f}^{{-{1}}}$. Write your answer using Interval Notation. Round to two decimal places as needed.

Domain of $\displaystyle {f}^{{-{1}}}$: