If f : [ 1 , ∞ ) → 1 , ∞ is defined by f x = 1 + 1 + 4 log 2 x 2 , then f - 1 3 =

Question

If f : [ 1 , ∞ ) → 1 , ∞ is defined by f x = 1 + 1 + 4 log 2 x 2 , then f - 1 3 =, 0, 1, 64, 1 + 5 2

MARKS App · Accepted Answer

f x = 1 + 1 + 4 log 2 x 2 If f x = y , then x = f - 1 y . 1 + 1 + 4 log 2 x 2 = y ⇒ 1 + 4 log 2 x = 2 y - 1 ⇒ 1 + 4 log 2 x = 4 y 2 + 1 - 4 y ⇒ log 2 x = y 2 - y ⇒ x = 2 y 2 - y f - 1 y = 2 y 2 - y ⇒ f - 1 3 = 2 3 2 - 3 = 2 9 - 3 = 2 6 = 64

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