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2022 AMC 10B Problem 24

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2022 AMC 10B Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Functions · difficulty 5 of 5 · about 7 min · position P21-25

Consider functions ff that satisfy ∣f(x)−f(y)∣≤12∣x−y∣|f(x)-f(y)|\leq \frac{1}{2}|x-y| for all real numbers xx and yy . Of all such functions that also satisfy the equation f(300)=f(900)f(300) = f(900) , what is the greatest possible value of f(f(800))−f(f(400))?f(f(800))-f(f(400))?

  1. A)

    2525

  2. B)

    5050

  3. C)

    100100

  4. D)

    150150

  5. E)

    200200

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