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To find the domain of the rational function \( R(x) = \frac{x}{x^3 - 27} \), we need to determine where the denominator is not equal to zero because division by zero is undefined.

1. **Set the denominator equal to zero:**  
   \[ x^3 - 27 = 0 \]

2. **Solve for \(x\):**  
   \[ x^3 = 27 \]  
   \[ x = \sqrt[3]{27} \]  
   \[ x = 3 \]

So, the denominator becomes zero when \( x = 3 \), which means that \( R(x) \) is undefined at \( x = 3 \).

Therefore, the domain of \( R(x) \) is all real numbers except \( x = 3 \). The correct choice is:

**A. The domain of \( R(x) \) is \( \{x \mid x \neq 3\} \).**

Would you like more details or have any questions? 

### Related Questions
1. How do you find the domain of a more complicated rational function?
2. What happens to the graph of a rational function at points where the function is undefined?
3. How does factoring the denominator help in finding the domain?
4. What are vertical asymptotes in the context of rational functions?
5. How do you solve for the roots of cubic equations?

### Tip:
Always check for values that make the denominator zero when determining the domain of a rational function.

Find the domain of the rational function R(x) = x / (x^3 - 27).

Learn how to find the domain of the rational function R(x) = x / (x^3 - 27). This problem involves understanding rational functions and identifying values that make the denominator zero. Suitable for students in Grades 9-11.

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