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

Step-by-step solution

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