https://file.aiquickdraw.com/mathbot/file/1725780234675wiy3iju3.jpg

To find the domain of the function \( f(x) = \frac{1}{2x - 10} \), we need to identify the values of \( x \) that make the denominator equal to zero, as the function will be undefined at these points.

### Step-by-step:
1. Set the denominator equal to zero:
   \[
   2x - 10 = 0
   \]
2. Solve for \( x \):
   \[
   2x = 10
   \]
   \[
   x = 5
   \]

So, the function is undefined at \( x = 5 \). This means that the domain excludes \( x = 5 \).

### Domain:
In interval notation, the domain is:
\[
(-\infty, 5) \cup (5, \infty)
\]

Let me know if you'd like more details or explanations. Here are a few follow-up questions to consider:

1. What happens to the function \( f(x) \) as \( x \) approaches 5 from the left and the right?
2. Can you explain why the function is undefined at \( x = 5 \)?
3. How would the domain change if the function had a different denominator, say \( 2x - 8 \)?
4. What is the range of this function given the domain we just found?
5. How do you find the vertical asymptote of a rational function?

**Tip:** Always check the denominator of a rational function to identify points where the function may be undefined.

Find the domain of the function f(x) = 1/(2x - 10).

Explore how to find the domain of the rational function f(x) = 1/(2x - 10) by setting the denominator to zero and solving for x. This tutorial is ideal for high school students learning about function domains and characteristics of rational functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation