Answer
$-\dfrac{2}{3}$
Work Step by Step
Value of certain composite functions formula:
$f(f^{-1}(x)) = \cos{(\cos^{-1}{x})}= x \hspace{25pt} -1 \leq x \leq 1$
$\therefore \cos{\left[\cos^{-1}{\left(-\dfrac{2}{3}\right)} \right]} = \boxed{-\dfrac{2}{3}}$
