To find the domain and range of the function $f(x) = \frac{x^2}{1 - x^2}$, let's go through the steps methodically.

Domain

The domain of a function is the set of all possible input values (x-values) that the function can accept without causing any mathematical problems (such as division by zero).

For the function $f(x) = \frac{x^2}{1 - x^2}$, we need to ensure that the denominator is not zero: $1 - x^2 \neq 0$ $x^2 \neq 1$ $x \neq \pm 1$

Thus, the domain is all real numbers except $x = \pm 1$: [