To determine the domain of the function [tex]\( f(x) = x^2 + x - 12 \)[/tex], we need to consider the type of function it is and identify any restrictions on [tex]\( x \)[/tex].
1. Type of Function:
- [tex]\( f(x) = x^2 + x - 12 \)[/tex] is a polynomial function.
2. Domain of Polynomial Functions:
- Polynomial functions are defined for all real numbers. There are no restrictions on the values that [tex]\( x \)[/tex] can take because polynomials are continuous and smooth curves on the real number line without any breaks, holes, or vertical asymptotes.
3. Conclusion:
- Since polynomial functions are defined for all real numbers, the domain of [tex]\( f(x) = x^2 + x - 12 \)[/tex] is all real numbers.
Therefore, the correct answer is:
(2) [tex]\( (-\infty, \infty) \)[/tex]
