To find the domain of the function $f(x) = 3 - x^2$, we need to determine the set of all possible values of $x$ for which the function is defined.

Since $f(x) = 3 - x^2$ is a polynomial function, and polynomial functions are defined for all real numbers, the domain of $f(x)$ is all real numbers.

Thus, the domain of $f(x) = 3 - x^2$ is:

$\text{Domain} = (-\infty, \infty)$

Would you like more details or have any questions? Here are some related questions:

1. What is the range of the function $f(x) = 3 - x^2$?
2. How do you find the vertex of the parabola represented by $f(x) = 3 - x^2$?
3. How would the domain change if the function were $f(x) = \sqrt{3 - x^2}$?
4. What is the derivative of $f(x) = 3 - x^2$?
5. How would you sketch the graph of $f(x) = 3 - x^2$?

Tip: For any polynomial function, the domain is always all real numbers unless there are specific restrictions (like division by zero or square roots of negative numbers).