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JEE Main202313 Apr 2023Morning ShiftMathematicsFunctionsActual

For the differentiable function f : ℝ - 0 - ℝ , let 3 f x + 2 f 1 x = 1 x - 10 , then f 3 + f ' 1 4 is equal to

Options

  1. A33 5
  2. B8
  3. C29 5
  4. D13

Correct answer

D. 13

Step-by-step solution

Given: 3 f x + 2 f 1 x = 1 x - 10       . . . . 1 Replace x → 1 x 3 f 1 x + 2 f x = x - 10       . . . . 2 Eliminating f 1 x from 1   &   2 , we get ⇒ 5 f x = 3 x - 2 x - 10 Let us replace x with 3 ⇒ 5 f 3 = 3 3 - 2 3 - 10 ⇒ f 3 = - 3 ⇒ 5 f ' x = - 3 x 2 - 2 ⇒ 5 f ' 1 4 = - 48 - 2 ⇒ f ' 1 4 = - 10 ⇒ f ( 3 ) + f ' 1 4 = 13 Hence this is the correct option.

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