What is the domain of the given function?

y=1/5x.

*

5 points

(-∞,∞)

(-∞,5)∪(5,∞)

(-∞,0)∪(0,∞)

(-∞,1/5)∪(1/5,∞)

The function provided is \( y = \frac{1}{5x} \).

### Analyzing the Function:
To find the domain of the function, we need to determine the values of \( x \) for which the function is defined.

- The function involves a division by \( 5x \).
- Division by zero is undefined, so the function is undefined when \( 5x = 0 \).

This implies:
\[ 5x = 0 \Rightarrow x = 0 \]

Therefore, the function is undefined at \( x = 0 \). For all other values of \( x \), the function is defined.

### Domain:
The domain of the function \( y = \frac{1}{5x} \) includes all real numbers except \( x = 0 \).

In interval notation, the domain is:
\[ (-\infty, 0) \cup (0, \infty) \]

### Correct Answer:
The correct option is:

**Option C: \( (-\infty, 0) \cup (0, \infty) \)**

---

Would you like further details or explanations? Here are some related questions:

1. How do you find the domain of a rational function?
2. What happens to the function \( y = \frac{1}{5x} \) as \( x \) approaches zero?
3. How do you express the domain of a function using interval notation?
4. Can a function have a domain that is all real numbers? Provide an example.
5. What is the difference between the domain and range of a function?
6. How do vertical asymptotes relate to the domain of a function?
7. How would the domain change if the function were \( y = \frac{1}{5(x-2)} \)?
8. What is the effect on the domain if a function is squared, such as \( y = \frac{1}{(5x)^2} \)?

**Tip:** Always watch out for division by zero or taking the square root of a negative number when determining the domain of a function.

Explore how to determine the domain of the function y = 1/(5x) with step-by-step explanation. Learn about rational functions and domain restrictions in mathematics. Suitable for high school students studying functions and algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation