SAT1000 - P153

Algebra Level 3

f(x)f(x) is a function defined at [0,1][0,1] such that:

  • f(0)=f(1)=0f(0)=f(1)=0.

  • x,y[0,1] (xy),f(x)f(y)<12xy\forall x,y \in [0,1]\ (x \neq y), |f(x)-f(y)| < \dfrac{1}{2} |x-y|.

If x,y[0,1],f(x)f(y)<k\forall x,y \in [0,1], |f(x)-f(y)|<k, find the minimum value of kk.

Let KK be the minimum value. Submit 1000K\lfloor 1000K \rfloor.

Have a look at my problem set: SAT 1000 problems


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