Question

find the domain of the following rational function.

\\g(x) = \frac{-7x^2}{(x - 5)(x + 6)}\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the domain of \\(g(x)\\) is restricted to
(type your answer in interval notation.)

b. the domain of \\(g(x)\\) has no restrictions.

Explanation:

Identify the domain condition

Using the Rational Functions and Domain Exclusion knowledge points

$$ (x-5)(x+6) eq 0 $$

Solve for excluded values

Using the Domain Exclusion knowledge point

$$
LATEXBLOCK0
$$

Express the domain in interval notation

The domain includes all real numbers except \(x = -6\) and \(x = 5\).
We write this set as the union of three open intervals:

$$ (-\infty, -6) \cup (-6, 5) \cup (5, \infty) $$

Answer:

• (A) The domain of g(x) is restricted to \((-\infty, -6) \cup (-6, 5) \cup (5, \infty)\) (Correct answer)
• (B) The domain of g(x) has no restrictions.