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The given function is:

\[
f(x) = \frac{9}{\sqrt[4]{x+13}} - 1
\]

### Step 1: Identify restrictions for the domain.
Since the function involves a fourth root, the expression inside the root must be non-negative to avoid complex numbers (since the even root of a negative number is not defined in the real number system). Therefore, we need the expression under the fourth root to be non-negative.

\[
x + 13 \geq 0
\]

### Step 2: Solve the inequality.
Solving for \( x \):

\[
x \geq -13
\]

### Step 3: Express the domain in interval notation.
The domain of the function is all \( x \) values that satisfy \( x \geq -13 \), which in interval notation is:

\[
[-13, \infty)
\]

Thus, the domain of the function is:

\[
[-13, \infty)
\]

Do you have any questions or would you like further details?

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Here are five related questions:
1. What is the domain of a square root function?
2. How does the domain change if the root is odd instead of even?
3. Can a fourth root have negative outputs for real numbers?
4. How do vertical asymptotes relate to the domain of a function like this?
5. What happens if the denominator equals zero in rational functions?

**Tip**: When working with roots, always remember that even roots (e.g., square or fourth roots) require non-negative radicands.

Find the domain of the following function: f(x) = 9 / 4√(x + 13) - 1.

This tutorial explains how to find the domain of the function f(x) = 9 / 4√(x + 13) - 1. Learn the steps to solve for x and express the domain in interval notation. This problem is suitable for students in Grades 10-12 studying Algebra.

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