Question
For the following two (02) items: Consider the function f(x) = x 1 - x (x > 0, x 1). What is (1 - x)f( x ) + xf( x + 1) equal to?
NDA
Mathematics
Functions
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. -f(x)
- B. f(x)
- C. x
- D. 0
Answer
D. 0
Step-by-step solution
Given f(x) = x 1 - x Substitute x in f(x): f( x ) = x 1 - x Substitute x + 1 in f(x): f( x + 1) = x + 1 1 - ( x + 1) = x + 1 - x Now, evaluate the given expression: (1 - x)f( x ) + xf( x + 1) = (1 - x) ( x 1 - x ) + x ( x + 1 - x ) Using 1 - x = (1 - x )(1 + x ): = (1 - x )(1 + x ) ( x 1 - x ) - x ( x + 1) = x (1 + x ) - x ( x + 1) = 0 Answer: 0
Related: Mathematics — Functions · All PYQ Banks