MathDB
1987 AMC 12 #24 - Functions

Source:

January 1, 2012
functionalgebrapolynomialAMC

Problem Statement

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=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> finitely many but more than 2<spanclass=latexbold>(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}