Multiple choice general knowledge math & puzzles

Let f(x) be a function satisfying f(x)f(y)=f(xy)for all real x,y.If f(2)=4,then what is the value of f(1/2)

  1. 0

  2. 1/2

  3. 1/4

  4. 1
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C Correct answer
Explanation

Given the functional equation f(x)f(y) = f(xy), we can substitute x = 1 and y = 1 to find f(1), or use test values. Letting x = 1/2 and y = 2 gives f(1/2)f(2) = f(1). Alternatively, using powers, if f(2) = 4, testing f(x) = x^2 yields f(1/2) = (1/2)^2 = 1/4.

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