Question

find the domain of the following rational function.

\\h(x) = \frac{x + 8}{x^2 - 64}\\

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

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

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

Explanation:

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<reasoning>

Identify the condition for domain restriction

Using the Rational Functions and Domain Exclusion knowledge points
\[
x^2 - 64
e 0
\]

Solve for the excluded values

Using the Domain Exclusion knowledge point
\[

$$\begin{aligned} x^2 & e 64 \\ x & e \pm 8 \end{aligned}$$

\]

Express the domain in interval notation

Using the Interval Notation knowledge point
\[
(-\infty, -8) \cup (-8, 8) \cup (8, \infty)
\]
</reasoning>

<answer>
<mcq-correct>(A) The domain of h(x) is restricted to \((-\infty, -8) \cup (-8, 8) \cup (8, \infty)\)</mcq-correct>
<mcq-option>(B) The domain of h(x) has no restrictions.</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the condition for domain restriction

Using the Rational Functions and Domain Exclusion knowledge points
\[
x^2 - 64
e 0
\]

Solve for the excluded values

Using the Domain Exclusion knowledge point
\[

$$\begin{aligned} x^2 & e 64 \\ x & e \pm 8 \end{aligned}$$

\]

Express the domain in interval notation

Using the Interval Notation knowledge point
\[
(-\infty, -8) \cup (-8, 8) \cup (8, \infty)
\]
</reasoning>

<answer>
<mcq-correct>(A) The domain of h(x) is restricted to \((-\infty, -8) \cup (-8, 8) \cup (8, \infty)\)</mcq-correct>
<mcq-option>(B) The domain of h(x) has no restrictions.</mcq-option>
</answer>

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