NDA 2026 · PYQ · Functions · medium
If 2f(x) + f(1-x) = x, then what is f(x) equal to?
- A.x - 1
- B.x - (1/3)✓ Correct
- C.2x
- D.2x - 1
Given 2f(x) + f(1-x) = x ...(1). Replace x with 1-x: 2f(1-x) + f(x) = 1-x ...(2). Multiply (1) by 2: 4f(x) + 2f(1-x) = 2x. Subtract (2): 4f(x) + 2f(1-x) - 2f(1-x) - f(x) = 2x - (1-x), giving 3f(x) = 3x - 1, so f(x) = x - 1/3.
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