Question

Find the domain of the following rational function.
h left parenthesis x right parenthesis equals StartFraction x plus 11 Over x squared minus 121 EndFraction
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Part 1
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
  
enter your response here.
​(Type your answer in interval​ notation.)
B.
The domain of​ h(x) has no restrictions.

Answer 1

To find the domain of the rational function \( h(x) = \frac{x + 11}{x^2 - 121} \), we need to determine where the function is defined. A rational function is undefined when the denominator is equal to zero.

First, we find the values of \( x \) that make the denominator zero:

\[
x^2 - 121 = 0
\]

We can factor this equation:

\[
x^2 - 121 = (x - 11)(x + 11) = 0
\]

Setting each factor equal to zero gives us the solutions:

\[
x - 11 = 0 \quad \Rightarrow \quad x = 11
\]
\[
x + 11 = 0 \quad \Rightarrow \quad x = -11
\]

Thus, the function \( h(x) \) is undefined at \( x = 11 \) and \( x = -11 \).

The domain of \( h(x) \) includes all real numbers except for \( x = 11 \) and \( x = -11 \). In interval notation, we can express the domain as:

\[
(-\infty, -11) \cup (-11, 11) \cup (11, \infty)
\]

So the correct choice is:

A. The domain of \( h(x) \) is restricted to \( (-\infty, -11) \cup (-11, 11) \cup (11, \infty) \).