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Lê Quốc Trần Anh Coordinator

15/08/2017 at 13:37
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If \(f\left(x\right)=\left\{{}\begin{matrix}\sqrt{x}\left(x\ge16\right)\\x+1\left(10< x< 16\right)\\\dfrac{x}{2}-10\left(0\le x\le10\right)\\x^2\left(x< 0\right)\end{matrix}\right.\) 

then what is the value of \(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(f\left(13\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\)?



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    Phan Thanh Tinh Coordinator 15/08/2017 at 13:52

    \(f\left(13\right)=14\)

    \(f\left(f\left(13\right)\right)=15\)

    \(f\left(f\left(f\left(13\right)\right)\right)=16\)

    \(f\left(f\left(f\left(f\left(13\right)\right)\right)\right)=4\)

    \(f\left(f\left(f\left(f\left(f\left(13\right)\right)\right)\right)\right)=-8\)

    \(f\left(f\left(f\left(f\left(f\left(f\left(13\right)\right)\right)\right)\right)\right)=64\)

    \(f\left(f\left(...\left(f\left(13\right)\right)\right)\right)=8\) (7 letters f)

                                    = -6 (8 letters f)

                                    = 36 (9 letters f)

                                    = 6 (10 letters f)

                                    = -7 (11 letters f)

                                    = 49 (12 letters f)

                                    = 7 (13 letters f)

    So,the answer is 7

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