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24

Part of 1987 AMC 12/AHSME

Problems(1)

1987 AMC 12 #24 - Functions

Source:

1/1/2012
How many polynomial functions ff of degree ≥1\ge 1 satisfy f(x2)=[f(x)]2=f(f(x)) ? f(x^2)=[f(x)]^2=f(f(x)) \ ? <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> finitely many but more than 2<spanclass=′latex−bold′>(E)</span> infinitely many <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ \text{finitely many but more than 2} \\ \qquad<span class='latex-bold'>(E)</span>\ \text{infinitely many}
functionalgebrapolynomialAMC