Number of functions f : 0 , 1 → 0 , 1 satisfying f x - f y = x - y for all x ,   y in 0 , 1 is

Step-by-step solution

Given, | f x - f y | = | x - y | for all in 0 , 1 ⇒ | f x - f y | | x - y | = 1 ⇒ lim x → y | f x - f y | x - y = 1 ⇒ f ' x = 1 ⇒ f ' x = ± 1 ⇒ f x = ± x x ∈ 0 , 1 ∴ f x has exactly 2 function.