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JEE Main202226 Jul 2022Morning ShiftMathematicsFunctionsActual

Let f : R → R be a continuous function such that f 3 x - f x = x . If f 8 = 7 , then f 14 is equal to:

Options

  1. A4
  2. B10
  3. C11
  4. D16

Correct answer

B. 10

Step-by-step solution

Given f 3 x - f x = x Now replance x   by  x 3 infinite times, f x - f x 3 = x 3 f x 3 - f x 3 2 = x 3 2 . . On adding, we get f x - lim n → ∞ f x 3 n = x 1 3 + 1 3 2 + ⋯ + ∞ f x - lim n → ∞ f x 3 n = x 1 3 1 - 1 3 = x 2 ⇒     f x - f 0 = x 2 Given f 8 = 7 so f 8 - f 0 = 4 i.e. f 0 = 3 ∴     f x = x 2 + 3 Hence f 14 = 10

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