Find the domain of the function. (Enter your answer using interval notation.)
f(x) = 
x/5x − 8

To find the domain of the function \( f(x) = \frac{x}{5x - 8} \), we need to determine the values of \( x \) for which the function is defined. The function will be undefined wherever the denominator is equal to zero, because division by zero is undefined.

1. **Set the denominator equal to zero**:
   \[
   5x - 8 = 0
   \]

2. **Solve for \( x \)**:
   \[
   5x = 8
   \]
   \[
   x = \frac{8}{5}
   \]

This means the function is undefined at \( x = \frac{8}{5} \).

3. **Domain**:
   The domain of the function is all real numbers except \( x = \frac{8}{5} \). In interval notation, the domain is:
   \[
   (-\infty, \frac{8}{5}) \cup (\frac{8}{5}, \infty)
   \]

So, the domain of \( f(x) = \frac{x}{5x - 8} \) is \(\boxed{(-\infty, \frac{8}{5}) \cup (\frac{8}{5}, \infty)}\).

Would you like a detailed explanation on any part of this solution, or do you have any other questions? 

Here are 5 related questions you might find interesting:
1. How do you find the domain of a function involving a square root?
2. What is the domain of the function \( f(x) = \frac{1}{x^2 - 9} \)?
3. How does the domain change if the function is \( f(x) = \frac{x + 3}{5x - 8} \)?
4. Can the domain of a function ever be all real numbers?
5. How do you determine the domain of a logarithmic function?

**Tip:** Remember, to find the domain of a rational function, always check where the denominator equals zero. These points are excluded from the domain.

Learn how to find the domain of the rational function f(x) = x / (5x - 8). This involves determining where the denominator is zero, which points are excluded from the domain, and representing the domain using interval notation. Suitable for high school students and beyond.

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