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Let f : R → 2 , ∞ be a function defined as f x = x 2 - 12 a x + 15 - 2 a + 36 a 2 . If f x is surjective on R , then the value of a is equal to

Options

  1. A9 2
  2. B11 2
  3. C13 2
  4. D15 2

Correct answer

C. 13 2

Step-by-step solution

Rewriting the given function, we get, f x = x - 6 a 2 + 15 - 2 a ∵ f x is surjective on R ⇒ 15 – 2 a = 2 ⇒ 2 a = 13 ⇒ a = 13 2

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