Find the Domain f(x)=|x-3|+4

Problem

ƒ(x)=|x−3|+4

Solution

1. Identify the type of function. The given function ƒ(x)=|x−3|+4 is an absolute value function.

2. Determine if there are any restrictions on the input variable x Absolute value functions are defined for all real numbers because there are no denominators that could be zero and no even-indexed roots of negative numbers.

3. Conclude that since the expression |x−3|+4 is defined for every real value of x the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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