Answer
$-3$
Work Step by Step
See: Inverse Function, p.409.
Let $f$ be a one-to-one function.
Then $g$ is the inverse function of $f$ if
$(f\circ g)(x)=x$ for every $x$ in the domain of $g$,
and $(g\circ f)(x)=x$ for every $x$ in the domain of $f$.
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$f^{-1}(6)=f^{-1}[f(-3)]=f^{-1}\circ f(-3)=$
by the definition,
$= -3$