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(1) f(4) equal to?

Question

Accepted Answer

9. From f(x/y) = f(x)/f(y), setting x = y gives f(1) = f(x)/f(x) = 1. f(4) = f(2·2). Using f(x) = x^k where 2^k = 3: f(4) = 4^k = (2^k)² = 9. Hence f(1)·f(4) = 1 × 9 = 9.

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(1) f(4) equal to?

Explanation

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