Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x+y) for all real values of x and y , and f(5) = 10 . What is f(0) equal to?

Step-by-step solution

Given the functional equation f(xy) = f(x+y) for all real values of x and y . Substituting y = 0 into the given equation: f(x 0) = f(x + 0) f(0) = f(x) This shows that f(x) is a constant function, meaning it takes the same value for all real x . We are given that f(5) = 10 . Since f(x) = f(0) for all x , substituting x = 5 gives: f(5) = f(0) Therefore, f(0) = 10 . Answer: 10