Question 13

Let $$f(x)\neq0$$ for any '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 $$f(\frac{1}{2})$$?

Solution

$$f(1)^2$$ = f(1) => f(1) = 1

f(2)*(f(1/2) = f(1) => 4x = 1

So, f(1/2) = 1/4

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