Fibonacci Reversed

Algebra Level 2

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

Let f 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 ) ) ) f^{-1}(f^{-1}(f^{-1}(13))) ?


The answer is 2.

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

By using inverse function f − 1 f^{-1} application, f − 1 ( 13 ) = 5 f^{-1}(13) = 5 . f − 1 ( 5 ) = 3 f^{-1}(5) = 3 . f − 1 ( 3 ) = 2 f^{-1}(3) = 2 .

Therefore, f − 1 ( f − 1 ( f − 1 ( 13 ) ) ) = 2 f^{-1}(f^{-1}(f^{-1}(13))) = \boxed{2} .

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Cool question and explanation doc!

Sravanth C. - 5 years, 3 months ago

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Thanks! Glad you like it. ;)

Worranat Pakornrat - 5 years, 3 months ago

Oh, it's remaining me ,x=f(y)

Gary Jiang - 4 years, 11 months ago

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