Determine the domain of the function. 
f left parenthesis x right parenthesis equals StartFraction 5 x minus 8 Over 5 x plus 15 EndFraction


To determine the domain of the function

\[
f(x) = \frac{5x - 8}{5x + 15},
\]

we need to identify the values of \(x\) for which the function is defined. A rational function like this is undefined when its denominator is equal to zero. So, we solve the equation:

\[
5x + 15 = 0.
\]

### Solving for \(x\):
\[
5x = -15 \quad \Rightarrow \quad x = -3.
\]

Thus, the function is undefined at \(x = -3\). Therefore, the domain of the function is all real numbers except \(x = -3\).

### The domain of \(f(x)\) is:
\[
\boxed{(-\infty, -3) \cup (-3, \infty)}.
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the domain of a square root function?
2. What is the range of this function \(f(x)\)?
3. How do you simplify rational functions?
4. How would the domain change if the denominator had multiple factors?
5. How can vertical asymptotes be related to domain restrictions?

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

Determine the domain of the function. f(x) = (5x - 8) / (5x + 15)

Learn how to find the domain of the rational function f(x) = (5x - 8) / (5x + 15). This guide covers solving for values that make the denominator zero and understanding domain restrictions for rational functions. Suitable for students in Grades 9-11.

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