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

Problem

ƒ(x)=|x|+|x−1|

Solution

1. Identify the type of function. The function ƒ(x) is the sum of two absolute value functions.

2. Determine the restrictions for absolute value functions. Absolute value functions are defined for all real numbers because the expression inside the absolute value, in this case x and x−1 can be any real value.

3. Check for potential domain restrictions such as denominators that could be zero, square roots of negative numbers, or logarithms of non-positive numbers. None of these restrictions are present in this expression.

4. Conclude that the function is defined for every real number x

Final Answer

Domain:(−∞,∞)

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