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(20) + f(-20) equal to?

Step-by-step solution

Given f(xy) = f(x+y) for all real values of x and y . Substituting y = 0 , we get f(x 0) = f(x + 0) , which simplifies to f(0) = f(x) for all real x . This implies that f(x) is a constant function for all real values of x . Since f(5) = 10 , the constant value of the function is 10 . Thus, f(x) = 10 for all x R . We need to find the value of f(20) + f(-20) . f(20) = 10 f(-20) = 10 f(20) + f(-20) = 10 + 10 = 20 Answer: 20