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(16) equal to?
NDA
Mathematics
Functions
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 18
- B. 27
- C. 54
- D. 81
Answer
D. 81
Step-by-step solution
Given f ( x y ) = f(x) f(y) Substituting x = 1 and y = 1, we get f(1) = 1 Substituting x = 1, we get f ( 1 y ) = f(1) f(y) = 1 f(y) Replacing y with 1 y in the given equation, we get: f(xy) = f(x) f ( 1 y ) = f(x)f(y) Using this property, f(16) = f(2^4) = (f(2))^4 Given f(2) = 3, we have f(16) = 3^4 = 81 Answer: 81
Related: Mathematics — Functions · All PYQ Banks