Answered

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The domain of the function [tex]f(x) = x^2 + x - 12[/tex] is:

1. [tex](-\infty, -4][/tex]
2. [tex](-\infty, \infty)[/tex]
3. [tex][-4, 3][/tex]
4. [tex][3, \infty][/tex]

Sagot :

GinnyAnsweridn
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]
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