Question 24
Consider functions $f$ that satisfy $$
|f(x)-f(y)|\leq \dfrac{1}{2}|x-y|
$$ for all real numbers $x$ and $y.$ Of all such functions that also satisfy the equation $f(300) = f(900),$ what is the greatest possible value of the following expression? $$
f(f(800))-f(f(400))
$$
|f(x)-f(y)|\leq \dfrac{1}{2}|x-y|
$$ for all real numbers $x$ and $y.$ Of all such functions that also satisfy the equation $f(300) = f(900),$ what is the greatest possible value of the following expression? $$
f(f(800))-f(f(400))
$$