Answer
Yes.
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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$(3,-4)$ is on the graph of f,
$(-4,3) $ is on the graph of g,
$(2,-6)$ is on the graph of f,
$(-6,2) $ is on the graph of g,
$(5,8)\quad\leftrightarrow\quad (8,5)$
$(1,9)\quad\leftrightarrow\quad (9,1)$
$(4,8)\quad\leftrightarrow\quad (3,4)$
... valid for all five pairs (x,f(x)), so
yes, they are inverses.
