Answer
$-\dfrac{2}{3}$
Work Step by Step
We know that $f(f^{-1}(x))=x$.
Hence,
$\cos\left(\cos^{-1}(-\frac{2}{3})\right)=-\frac{2}{3}.$
We also need that $-1 \leq x\leq 1$, which is true here.
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