The function provided is:

$f(x) = |1 + 3x|$

To find the domain of $f(x)$, we need to determine for which values of $x$ the expression inside the absolute value function is defined.

The absolute value function $|1 + 3x|$ is defined for all real numbers, because the expression inside the absolute value, $1 + 3x$, is a linear function, and a linear function is defined for all real values of $x$.

Thus, the domain of $f(x) = |1 + 3x|$ is all real numbers.

In interval notation, the domain is:

$(-\infty, \infty)$

Would you like further details on absolute value functions or their domains?

Here are some related questions to expand your understanding:

1. How do absolute value functions behave graphically?
2. What is the domain of the function $f(x) = \sqrt{x - 3}$?
3. What is the range of the function $f(x) = |x - 4| + 2$?
4. How can you solve equations involving absolute value expressions?
5. What is the difference between the domain of a rational function and an absolute value function?

Tip: Remember that absolute value functions are defined for all real numbers, so their domain is typically $(-\infty, \infty)$.