Question
For the following two (02) items: Consider the function f(x) = x 1 - x (x > 0, x 1). What is f(x) f(x+1) equal to?
NDA
Mathematics
Functions
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. -f(x^2)
- B. -f( x )
- C. f(x^2)
- D. f(x - 1)
Answer
A. -f(x^2)
Step-by-step solution
Given f(x) = x 1 - x Substitute x+1 for x to find f(x+1): f(x+1) = x+1 1 - (x+1) = x+1 -x Now, calculate the ratio f(x) f(x+1) : f(x) f(x+1) = x 1 - x x+1 -x f(x) f(x+1) = x 1 - x -x x+1 = -x^2 1 - x^2 Since f(x^2) = x^2 1 - x^2 , we get: f(x) f(x+1) = -f(x^2) Answer: -f(x^2)
Related: Mathematics — Functions · All PYQ Banks