Fibonacci Reversed

Algebra Level 2

\[\begin{cases} f(1) = 2 \\ f(2) = 3 \\ f(3) = 5 \\ f(4) = 8 \\ f(5) = 13 \end{cases}\]

Let \(f\) be the function with one-to-one relation similar to the Fibonacci sequence as shown above.

What is the value of \(f^{-1}(f^{-1}(f^{-1}(13)))\)?

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