Let f : R - α 6 → R be defined by f x = 5 x + 3 6 x - α . Then the value of α for which f o f x = x , for all x ∈ R - α 6 , is

Question

Let f : R - α 6 → R be defined by f x = 5 x + 3 6 x - α . Then the value of α for which f o f x = x , for all x ∈ R - α 6 , is, No such α exists, 5, 8, 6

MARKS App · Accepted Answer

We have, f x = y = 5 x + 3 6 x - α … i ⇒ 5 x + 3 = 6 x y - α y ⇒ x ( 6 y - 5 ) = α y + 3 ⇒ x = α y + 3 6 y - 5 Hence, f - 1 x = α x + 3 6 x - 5 … ii Now, f o f x = x f ( x ) = f - 1 ( x ) From equation i and i i , we have 5 x + 3 6 x - α = α x + 3 6 x - 5 Clearly, α = 5

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