Let f(x)f(y)=f(xy) for <strong>ALL</strong> real x, y. If f(2)=4 then what is the value of f(1/2)?

Explanation

The given functional equation f(x)f(y) = f(xy) for all real numbers indicates a power function of the form f(x) = x^n. Given f(2) = 4, we deduce 2^n = 4, which means n = 2. Therefore, f(x) = x^2. Evaluating at x = 1/2, we get f(1/2) = (1/2)^2 = 1/4.

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