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
f(f(800))-f(f(400)) ?
Answer Choices
A. 25
B. 50
C. 100
D. 150
E. 200