If f x + 2 f 1 - x = 6 x ∀ x ∈ R , then the value of 3 4 f 8 f ' 1 is equal to

Question

If f x + 2 f 1 - x = 6 x ∀ x ∈ R , then the value of 3 4 f 8 f ' 1 is equal to,

MARKS App · Accepted Answer

In given equation substituting x by 1 - x , we get, f 1 - x + 2 f 1 - 1 - x = 6 1 - x f 1 - x + 2 f x = 6 - 6 x From these two equations, we get, f x + 2 6 - 6 x - 2 f x = 6 x - 3 f x + 12 - 12 x = 6 x 3 f x = 12 - 18 x ⇒ f x = 4 - 6 x f 8 = - 44 , f ' 1 = - 6 f 8 f ' 1 = - 44 - 6 = 22 3

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