Consider the following for the two (02) items that follow: 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?

Step-by-step solution

Given f ( x y ) = f(x) f(y) for all x, y > 0 . Substituting x = 1 and y = 1 , we get: f(1) = f(1) f(1) f(1) = 1 Substituting x = 4 and y = 2 , we get: f ( 4 2 ) = f(4) f(2) f(2) = f(4) f(2) f(4) = (f(2))^2 Since f(2) = 3 , we have f(4) = 3^2 = 9 . Therefore, f(1)f(4) = 1 9 = 9 . Answer: 9