Library / KöMaL problem A / 4 of 136
KöMaL problem A, 2023 Difficulty 5.0 AIME, harder Prove it Hungary
Let f ( x ) = x 2 − 2 f(x)=x^2-2 f ( x ) = x 2 − 2 f ( n ) ( x ) f^{(n)}(x) f ( n ) ( x ) n th n^{\text{th}} n th f f f f ( 1 ) ( x ) = f ( x ) f^{(1)}(x)=f(x) f ( 1 ) ( x ) = f ( x ) f ( k + 1 ) ( x ) = f ( f ( k ) ( x ) ) f^{(k+1)}(x)=f\big(f^{(k)}(x)\big) f ( k + 1 ) ( x ) = f ( f ( k ) ( x ) )
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