If the function f: R - \ 1, - 1\ → A defined by f(x) = x ^ 2 1 - x...

A function is surjective, when the range of the function is same as the co-domain.

Now, $y = \dfrac{{x}^{2}}{1 - {x}^{2}}$

$⇒ y - y{x}^{2} = {x}^{2}$

$⇒ y = {x}^{2}\left(y + 1\right)$

$⇒ {x}^{2} = \dfrac{y}{y + 1}$

$∵ {x}^{2} \ge 0 ⇒ \dfrac{y}{y + 1} \ge 0$

$⇒ y \in \left(- \infty , - 1\right) \cup \left[0, \infty\right)$ or $R - \left[- 1, 0\right) .$

$∴$ Range of $f = A = R - \left[- 1, 0\right) .$