# $$f^{-1}(g^{-1})$$

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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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