Let f(x) be a function satisfying f(x) × f(y) = f(xy) for all real x, y. Let f(2) = 4, then what is the value of f12?
Explanation:
Given, f(x) × f(y) = f(xy)
Let x = 1 and y = 2
∴ f(1) × f(2) = f(2) ∴ f(1) = 1
Now, let x = 1/2 and y = 2
∴ f(1/2) × f(2) = f(1/2 × 2) = f(1)
∴ f(1/2) × 4 = 1
∴ f(1/2) = 1/4
Hence, option (b).
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