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NDA 2025 · PYQ · Functional equations · medium

The function f(x) satisfies f(x/y) = f(x)/f(y) for all positive real values of x and y, and f(2) = 3. What is f(16) equal to?

  1. A.18
  2. B.27
  3. C.54
  4. D.81✓ Correct

Explanation

The functional equation f(x/y) = f(x)/f(y) suggests f(x) = x^k for some k. f(2) = 2^k = 3, so 2^k = 3. Then f(16) = 16^k = (2^4)^k = (2^k)^4 = 3^4 = 81.
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