\[
f(x)=|x| \text { and } g(x)=-4 x
\]
Step 2 of 2: Find the domain for $\left(\frac{f}{g}\right)(x)$. Express your answer in interval notation.
Answer
Domain:

Step 1 ：Define the functions f(x) = |x| and g(x) = -4x.

Step 2 ：The domain of a function is the set of all possible input values (x-values) which will produce a valid output. For the function \(\frac{f}{g}(x)\), we need to find all x-values for which both f(x) and g(x) are defined and g(x) is not equal to zero (since we cannot divide by zero).

Step 3 ：The function f(x) = |x| is defined for all real numbers, so its domain is all real numbers.

Step 4 ：The function g(x) = -4x is also defined for all real numbers, but it equals zero when x = 0.

Step 5 ：Therefore, the domain of \(\frac{f}{g}(x)\) is all real numbers except 0.

Step 6 ：\(\boxed{(-\infty, 0) \cup (0, \infty)}\) is the final answer, which is the domain of \(\frac{f}{g}(x)\) expressed in interval notation.