To find the domain of the function:

$f(x) = 2 - 3x^2$

Step 1: Identify Restrictions

The domain of a function includes all values of $x$ for which the function is defined. In this case:

• The function $f(x)$ is a polynomial (a quadratic function).
• Polynomial functions are defined for all real numbers because they do not involve division by zero or square roots of negative numbers.

Step 2: Conclusion

Since there are no restrictions on $x$, the domain of $f(x)$ is:

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

or in set notation:

$\{ x \in \mathbb{R} \}$

Would you like further explanation or a graphical interpretation?

Related Questions:

1. What is the range of $f(x) = 2 - 3x^2$?
2. How do you find the vertex of $f(x) = 2 - 3x^2$?
3. What are the intercepts of $f(x) = 2 - 3x^2$?
4. How do you determine if $f(x) = 2 - 3x^2$ is increasing or decreasing?
5. What is the axis of symmetry for $f(x) = 2 - 3x^2$?

Tip:

For quadratic functions in the form $ax^2 + bx + c$, the domain is always all real numbers unless there are explicit constraints in a problem.