# Difference between revisions of "1984 AIME Problems/Problem 12"

## Problem

A function $\displaystyle f$ is defined for all real numbers and satisfies $\displaystyle f(2+x)=f(2-x)$ and $\displaystyle f(7+x)=f(7-x)$ for all $\displaystyle x$. If $\displaystyle x=0$ is a root for $\displaystyle f(x)=0$, what is the least number of roots $\displaystyle f(x)=0$ must have in the interval $\displaystyle -1000\leq x \leq 1000$?