NDA 2024 · PYQ · Functional Equations · medium
Let 3f(x) + f(1/x) = 1/x + 1. What is f(x) equal to?
- A.1/(8x) - x/8 + 1/4
- B.3/(8x) - x/8 + 3/4
- C.3/(8x) + x/8 + 1/4
- D.3/(8x) - x/8 + 1/4✓ Correct
Given 3f(x) + f(1/x) = 1/x + 1 ... (i). Replace x by 1/x: 3f(1/x) + f(x) = x + 1 ... (ii). Multiply (i) by 3: 9f(x) + 3f(1/x) = 3/x + 3. Subtract (ii): 9f(x) - f(x) = 3/x + 3 - x - 1, so 8f(x) = 3/x - x + 2. Therefore f(x) = 3/(8x) - x/8 + 1/4.
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