\(f^{-1}(g^{-1})\)

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Functions \(f\) and \(g\) are defined as follows: \[\begin{align} f(x) &= \begin{cases} x^2-18x+3 & (x \geq 1) \\ x+1 & (x<1), \end{cases} \\ g(x) &= -x+24. \end{align} \] What is the value of \(f^{-1}(g^{-1}(2))\)?

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