To find the domain of the function \( f(x) = \frac{5}{2x + 5} \), we need to determine the values of \(x\) for which the function is defined.

Since the function involves a fraction, it is undefined when the denominator is equal to zero. So, we need to solve for \(x\) when the denominator equals zero:

\[
2x + 5 = 0
\]

Solve for \(x\):

\[
2x = -5
\]
\[
x = -\frac{5}{2}
\]

Thus, the function is undefined at \( x = -\frac{5}{2} \). Therefore, the domain of the function is all real numbers except \(x = -\frac{5}{2}\).

In interval notation, the domain is:
\[
(-\infty, -\frac{5}{2}) \cup (-\frac{5}{2}, \infty)
\]

Would you like more details or have any questions?

Here are some related questions:
1. What is the range of the function \( f(x) = \frac{5}{2x + 5} \)?
2. How do you find the asymptotes of a rational function like \( f(x) = \frac{5}{2x + 5} \)?
3. What happens to the value of \( f(x) \) as \( x \to \infty \) or \( x \to -\infty \)?
4. Can you determine the inverse of the function \( f(x) = \frac{5}{2x + 5} \)?
5. How does the graph of \( f(x) = \frac{5}{2x + 5} \) behave near the point \( x = -\frac{5}{2} \)?

**Tip:** When finding the domain of a rational function, always check for values that make the denominator zero!

Learn how to find the domain of the rational function f(x) = 5/(2x + 5) by solving the equation where the denominator equals zero. This detailed explanation covers key algebraic concepts, including domain restrictions for rational functions. Suitable for Grades 9-10 students.

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