Let f : 0 , 1 → R be an injective continuous function that satisifes the condition - 1 < f 0 < f 1 < 1 Then, the number of functions g : - 1 , 1 → 0 , 1 such that g o f x = x for all x ∈ 0 , 1 is

Step-by-step solution

We have, - 1 < f 0 < f 1 < 1 g = - 1 , 1 → 0 , 1 gof x = x , ∀ x ∈ 0 , 1 Only condition that g x should satisfy for g o f x = x , ∀ x ∈ 0 , 1 is that g x should attain all values in 0 , 1 when range of f x a subset of - 1 , 1 is used as image for g x . Thus, there can be infinite such functions g x with domain - 1 , 1 and range 0 , 1