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

Question

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, 9 2, 11 2, 13 2, 15 2

MARKS App · Accepted Answer

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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