https://file.aiquickdraw.com/mathbot/file/17275444587716kd25090.jpg

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 \( (-\infty, \infty) \).

Give the domain of f(x) = |1 + 3x| using interval notation.

Learn how to find the domain of the absolute value function f(x) = |1 + 3x|. This tutorial covers algebraic concepts involving the properties of absolute value functions and provides a detailed step-by-step explanation suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation