Question

select the correct answer.

what is the domain of (f(x) = |x - 1| + 3)?

• (-infty < x < 1)
• (3 le x < infty)
• (-infty < x le -1)
• all real numbers

Explanation:

🆕 New Concept Discovered: Domain of Absolute Value Functions
The set of all possible input values.

Step 1: Identify the function type

The given function is:

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

This is an absolute value function.

Step 2: Determine restrictions on the input variable

The domain of a function is the set of all possible input values (\(x\)-values) for which the function is defined and produces a real number.

We look for operations that restrict the domain, such as:

• Division by zero (denominators cannot be zero)
• Even roots of negative numbers (terms under a square root must be non-negative)

In the expression \(|x - 1| + 3\), there are no fractions and no square roots. We can plug in any real number for \(x\), subtract \(1\), take the absolute value, and add \(3\) without any mathematical errors.

Step 3: Write the domain

Since there are no restrictions on \(x\), the domain is all real numbers.

Answer:

all real numbers