NDA Mathematics Question (2025) — Solution

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