Question 12
A function $f$ is defined for all real numbers and satisfies $$
\begin{aligned} f(2+x)&=f(2-x),\\ f(7+x)&=f(7-x) \end{aligned}
$$ for all real $x.$ If $x=0$ is a root of $f(x)=0,$ what is the least number of roots $f(x)=0$ must have in the interval $-1000\leq x\leq1000?$
\begin{aligned} f(2+x)&=f(2-x),\\ f(7+x)&=f(7-x) \end{aligned}
$$ for all real $x.$ If $x=0$ is a root of $f(x)=0,$ what is the least number of roots $f(x)=0$ must have in the interval $-1000\leq x\leq1000?$