The function given is \( f(x) = \sqrt[3]{x+4} \), which is a cube root function.

### Domain Analysis:
- Cube roots, unlike square roots, can accept both positive and negative values as inputs.
- The cube root function \( \sqrt[3]{x} \) is defined for all real numbers \( x \), meaning there are no restrictions on the input.

Thus, the function \( \sqrt[3]{x+4} \) is defined for all real values of \( x \), because there are no values of \( x \) that would make the expression inside the cube root undefined.

### Domain:
The domain of \( f(x) = \sqrt[3]{x+4} \) is:
\[
\boxed{(-\infty, \infty)}
\]

Would you like any further explanation on cube roots or domains?

Here are 5 related questions:
1. What is the domain of \( \sqrt{2x - 5} \)?
2. What is the range of \( f(x) = \sqrt[3]{x+4} \)?
3. How would the domain change for \( f(x) = \sqrt{x+4} \)?
4. What is the graph of \( f(x) = \sqrt[3]{x+4} \) like?
5. How do cube roots differ from square roots in terms of their domain and range?

**Tip:** Cube root functions are always defined for all real numbers, while square root functions are only defined for non-negative numbers under the square root.

Discover the domain of the cube root function \sqrt[3]{x+4}. This algebra problem involves analyzing the domain of cube root functions, which are defined for all real numbers. Suitable for students in Grades 9-12, this solution provides a step-by-step explanation.

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