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.