Find the domain of the function.
f left parenthesis x right parenthesis equals StartFraction 13 Over x plus 11 EndFractionf(x)=
13
x+11

The given function is:

\[
f(x) = \frac{13}{x + 11}
\]

To find the domain of the function, we need to identify all values of \( x \) for which the function is defined. Since the function involves a fraction, we must ensure that the denominator is not equal to zero because division by zero is undefined.

The denominator is \( x + 11 \), so we set:

\[
x + 11 \neq 0
\]

Solving this inequality:

\[
x \neq -11
\]

Thus, the domain of the function is all real numbers except \( x = -11 \).

In interval notation, the domain is:

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

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the range of the function \( f(x) = \frac{13}{x + 11} \)?
2. How do you find vertical asymptotes for rational functions like this one?
3. What happens to \( f(x) \) as \( x \to -11 \)?
4. How would you graph the function \( f(x) = \frac{13}{x + 11} \)?
5. Can you find the inverse of the function \( f(x) = \frac{13}{x + 11} \)?

**Tip**: Always check the denominator of a rational function when determining the domain to avoid division by zero.

Find the domain of the function f(x) = 13 / (x + 11).

Learn how to determine the domain of the rational function f(x) = 13 / (x + 11). This step-by-step solution explains key algebraic concepts such as rational functions and how to avoid division by zero. Suitable for students in Grades 9-11.

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