For a bijective function $g : \mathbb{R} \to \mathbb{R}$, we say that a function $f : \mathbb{R} \to \mathbb{R}$ is its superinverse if it satisfies the following identity: 
\[(f \circ g)(x) = g^{-1}(x)\]
where $g^{-1}$ is the inverse of $g$. Given:
\[g(x) = x^3 + 9x^2 + 27x + 81\]
and $f$ is its superinverse, find:
\[|f(-289)|\]

Let's think step by step and output the final answer within \boxed{}.
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