Question
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?
NDA
Mathematics
Functions
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 4
- B. 8
- C. 9
- D. 18
Answer
C. 9
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
Related: Mathematics — Functions · All PYQ Banks