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We are tasked with finding the domain of the function \( g(x) = \frac{2}{10 - 7x} \).

### Steps to find the domain:
1. The function involves a rational expression, so we need to ensure that the denominator does not equal zero.
2. Set the denominator equal to zero and solve for \( x \):
   \[
   10 - 7x = 0
   \]
   \[
   7x = 10
   \]
   \[
   x = \frac{10}{7}
   \]
   Therefore, \( g(x) \) is undefined at \( x = \frac{10}{7} \).

### Conclusion:
The domain of the function consists of all real numbers except \( x = \frac{10}{7} \).

### Correct Option:
The correct answer is **A.** \( \{ x \mid x \text{ is a real number and } x \neq \frac{10}{7} \} \).

Would you like more details on this? Here are some related questions you might find useful:

1. How do you determine the domain of a rational function in general?
2. Why does the denominator being zero make a function undefined?
3. Can there be more than one value excluded from the domain of a rational function?
4. How does the domain change for more complex functions involving square roots?
5. What is the difference between the range and the domain of a function?

**Tip**: When finding the domain of a rational function, always start by identifying values that make the denominator zero, as these are excluded from the domain.

Find the domain of the function. g(x) = 2 / (10 - 7x). Choose the correct domain from the options below.

Learn how to find the domain of the rational function g(x) = 2 / (10 - 7x). This problem explains key algebraic concepts including how to handle rational functions and the importance of ensuring the denominator is not zero. Suitable for students in Grades 9-12.

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