MathDB

12

Part of 1984 AIME Problems

Problems(1)

Yet Another Function

Source:

12/19/2005
A function ff is defined for all real numbers and satisfies f(2+x)=f(2−x)andf(7+x)=f(7−x)f(2 + x) = f(2 - x)\qquad\text{and}\qquad f(7 + x) = f(7 - x) for all real xx. If x=0x = 0 is a root of f(x)=0f(x) = 0, what is the least number of roots f(x)=0f(x) = 0 must have in the interval −1000≤x≤1000-1000 \le x \le 1000?
functionmodular arithmeticfloor functiongeometrygeometric transformationreflection