Answer
no
Work Step by Step
See: Important Facts about Inverses, p.414,
1. If $f$ is one-to-one, then $f^{-1}$ exists.
2. The domain of $f$ is the range of $f^{-1}$, and the range of $f$ is the domain of $f^{-1}$.
3. If the point $(a, b)$ lies on the graph of $f$, then $(b, a)$ lies on the graph of $f^{-1}$.
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$(-1,-1)$ is on the graph of f,
BUT
$(-1,1) $ is on the graph of g, not $(-1,-1).$
So,
$g(f(-1))=1\neq-1$
meaning that f and are not inverses.
