Single correct option
A function f satisfies f(x) + 2f(1/x) = 3x + 1 for every non-zero real x. What is f(3)?
- A. −4
- B. −2
- C. 1
- D. 3
Show answer and solution
Answer: (B) −2
Put x = 3: f(3) + 2f(1/3) = 10 …(i)
Put x = 1/3: f(1/3) + 2f(3) = 2 …(ii)
Let a = f(3) and b = f(1/3). From (ii), b = 2 − 2a. Substitute into (i): a + 2(2 − 2a) = 10 → a + 4 − 4a = 10 → −3a = 6 → a = −2.
Tip: For equations linking f(x) and f(1/x), substitute x → 1/x to get a second equation and eliminate one function value.
Put x = 1/3: f(1/3) + 2f(3) = 2 …(ii)
Let a = f(3) and b = f(1/3). From (ii), b = 2 − 2a. Substitute into (i): a + 2(2 − 2a) = 10 → a + 4 − 4a = 10 → −3a = 6 → a = −2.
Tip: For equations linking f(x) and f(1/x), substitute x → 1/x to get a second equation and eliminate one function value.
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