The function given is $f(x) = 14(x - 4)$.

This is a linear function because it has the form $f(x) = mx + b$, which is a straight-line equation. Linear functions have no restrictions on the values of $x$ that can be used, meaning the domain of the function includes all real numbers.

Now, let’s examine the answer choices:

• A. $(-\infty, \infty)$: This represents all real numbers, which is correct for a linear function.
• B. $(-\infty, 0) \cup (0, \infty)$: This excludes $x = 0$, which is not a necessary restriction for this function.
• C. $(-\infty, 0) \cup (0, 4) \cup (4, \infty)$: This excludes $x = 0$ and $x = 4$, which again is not necessary.
• D. $(-\infty, 4) \cup (4, \infty)$: This excludes $x = 4$, which is not necessary since $x = 4$ is valid for this linear function.

Therefore, the correct answer is A. $(-\infty, \infty)$.

Would you like further explanation or have any questions?

Here are 5 related questions to explore further:

1. How would the domain change if there was a square root in the function?
2. What is the range of a linear function like $f(x) = 14(x - 4)$?
3. How do you find the domain of a rational function?
4. What is the effect of including a logarithm in the function for determining the domain?
5. How does a quadratic function's domain compare to that of a linear function?

Tip: The domain of a function tells you all the possible input values (values of $x$) that will not result in any mathematical contradictions such as division by zero or taking the square root of a negative number.