Find the Domain f(x)=|x-1|

Problem

ƒ(x)=|x−1|

Solution

1. Identify the type of function. The function ƒ(x)=|x−1| is an absolute value function.

2. Analyze the expression inside the absolute value. The expression x−1 is a polynomial (specifically a linear function).

3. Determine any restrictions. Polynomials and absolute value functions are defined for all real numbers. There are no denominators that could be zero and no even-indexed roots of negative numbers.

4. Conclude the domain. Since there are no values of x that make the expression undefined, the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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