Let A = x ∈ R : x is not a positive integer . Define a function f : A → R as f x = 2 x x - 1 , then f is:

Step-by-step solution

Given, function f x = 2 x x - 1 and domain of f x is - ∞ ,   0 Now f ' x = x - 1 2 - 2 x 1 - 0 x - 1 2 f ′ x = - 2 x - 1 2 < 0 ⇒ f is always decreasing in the given domain. Clearly, given function is one-one or injective. Since, codomain - ∞ ,   ∞ ≠ Range 0 ,   2 , hence f is into.