Find the domain of the function.

Write your answer in interval notation. Use inf for .

Question

Find the domain of the function.

Write your answer in interval notation.  Use inf for .

BlackTom AI · Accepted Answer

The prompt asks for the domain of the function and to express the answer in interval notation, but there are no answer choices provided to analyze. We can still discuss what the given domain suggestion implies and what information would typically determine a domain.

First, consider the proposed domain (-∞, -5) ∪ (-5, ∞). This domain excludes the single point x = -5, meaning the function is undefined at x = -5 but defined for every other real number. Such a domain commonly arises when the function has a factor in the denominator that becomes zero at x = -5, for example something like 1/(x + 5) or any expression where x = -5 creates a division by zero.

Second, compare with other standard domain possibilities:
- If the function involved a square root like sqrt(x + 5), the domain would require x + 5 ≥ 0, i.e., x ≥ -5, which would be the interval [-5, ∞), not the union shown.
- If the function had a square root in the denominator or a radical with a variable inside that would force restrictions, the domain could be different, possibly excluding more points.
- If the function were a polynomial or a rational function where the denominator does not vanish at -5, then -5 would be included in the domain, contradicting the proposed domain.

Third, the only information we can reliably infer here is that the domain excludes x = -5 while including all other real numbers. This aligns with a common pattern where a denominator contains (x + 5) or where a removable discontinuity has been introduced at x = -5 and simplified away in the expression.

Because there are no listed answer choices to judge, we cannot evaluate correctness against alternatives. If you have the original function, we could pinpoint the exact domain by identifying where the expression is defined (no division by zero, no square roots of negative numbers, etc.) and then translate that into interval notation. Remember to verify whether any discontinuities are removable (holes) or vertical asymptotes, as those distinctions affect domain differently.

Find the domain of the function. Write your answer in interval notation. Use inf for .

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