The range of the real valued function f x = x 2 + 2 x + 8 x 2 + 2 x + 4 is

Question

The range of the real valued function f x = x 2 + 2 x + 8 x 2 + 2 x + 4 is, 7 3 , ∞, 0 , ∞, 1 , ∞, 1 , 7 3

MARKS App · Accepted Answer

Given f x = x 2 + 2 x + 8 x 2 + 2 x + 4 = 1 + 4 x 2 + 2 x + 4 = 1 + 4 x + 1 2 + 3 We know, 3 ≤ x + 1 2 + 3 ∞ ⇒ 0 4 x + 1 2 + 3 ≤ 4 3 ⇒ 1 1 + 4 x + 1 2 + 3 ≤ 7 3 ⇒ 1 1 + 4 x + 1 2 + 3 ≤ 7 3 Hence, range of f x will be ( 1 , 7 3 ]

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