Answer
-1
Work Step by Step
We are given the expression: $\cos (\cos^{-1} \left(-1\right))$
$y=\cos^{-1} x$ is the value of $y$ so that $\cos y=x$, where $0\leq y\leq\pi$.
For $y\in[0,\pi]$, we have:
$f^{-1}(f(y))=f(f^{-1})(y)=y$
$\cos(\cos^{-1}(x))=x$, where $x\in[-1,1]$
So we get:
$\cos(\cos^{-1}(-1))=-1$
