To find the domain of the function \( f(x) = \frac{1}{1 - 7x} \), we need to determine the values of \( x \) for which the function is defined.

Since \( f(x) \) is a rational function, it is undefined where the denominator is zero. In this case, the denominator is \( 1 - 7x \). We need to find the value of \( x \) that makes the denominator zero:

\[
1 - 7x = 0
\]

Solving for \( x \), we get:

\[
7x = 1 \implies x = \frac{1}{7}
\]

Thus, the function \( f(x) = \frac{1}{1 - 7x} \) is undefined when \( x = \frac{1}{7} \). Therefore, the domain of \( f(x) \) includes all real numbers except \( x = \frac{1}{7} \).

**Domain of \( f(x) \):**

\[
\boxed{(-\infty, \frac{1}{7}) \cup (\frac{1}{7}, \infty)}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the domain of \( g(x) = \frac{3}{2x + 5} \)?
2. How do you find the domain of a function with both a square root and a fraction, like \( h(x) = \frac{\sqrt{x+2}}{x-3} \)?
3. What are the general rules for finding the domain of a logarithmic function, such as \( k(x) = \log(x - 1) \)?
4. How does the presence of an exponent in the denominator, such as \( m(x) = \frac{1}{x^2 - 1} \), affect the domain?
5. What is the domain of the function \( f(x) = \frac{1}{x^2 + 1} \)? 

**Tip:** Always set the denominator of a rational function not equal to zero to find the domain.

Discover how to find the domain of the function f(x) = 1 / (1 - 7x) step-by-step. This problem involves determining where a rational function is defined and explores the concept of domain in mathematics. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation