MathDB
Period of a Function that Satisfies an Equation

Source:

January 18, 2009
function

Problem Statement

Consider those functions f f that satisfy f(x \plus{} 4) \plus{} f(x \minus{} 4) \equal{} f(x) for all real x x. Any such function is periodic, and there is a least common positive period p p for all of them. Find p p. <spanclass=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 12<spanclass=latexbold>(C)</span> 16<spanclass=latexbold>(D)</span> 24<spanclass=latexbold>(E)</span> 32 <span class='latex-bold'>(A)</span>\ 8\qquad <span class='latex-bold'>(B)</span>\ 12\qquad <span class='latex-bold'>(C)</span>\ 16\qquad <span class='latex-bold'>(D)</span>\ 24\qquad <span class='latex-bold'>(E)</span>\ 32