If the function f : R - 1 , - 1 → A defined by f x = x 2 1 - x 2 , is surjective, then A is equal to

Step-by-step solution

A function is surjective, when the range of the function is same as the co-domain. Now, y = x 2 1 - x 2 ⇒ y - y x 2 = x 2   ⇒ y = x 2 y + 1 ⇒ x 2 = y y + 1 ∵     x 2 ≥ 0   ⇒ y y + 1 ≥ 0 ⇒ y   ∈ - ∞ ,   - 1 ∪ 0 ,   ∞ or R - − 1 ,   0 . ∴ Range of f = A = R - − 1 ,   0 .