Understanding the Domain in Mathematics | Definition, Notation, and Examples

domain

In mathematics, the domain refers to the set of all possible input values (or independent variables) for a function or relation

In mathematics, the domain refers to the set of all possible input values (or independent variables) for a function or relation. It represents the values for which the function is defined or meaningful.

The domain is often expressed using interval notation or as specific values depending on the nature of the function. For example:
– For a basic polynomial function like f(x) = x^2, the domain is the set of all real numbers (-∞, ∞) since the function is defined for any value of x.
– For a rational function like f(x) = 1/(x+2), the domain would exclude the value -2 since division by zero is undefined. So, the domain is (-∞, -2) U (-2, ∞).
– For a square root function like f(x) = √(x-3), the domain ensures that the expression inside the square root is non-negative. So, the domain is [3, ∞), since x must be at least 3 for the function to be defined.

It’s important to identify the domain of a function or relation, as it helps determine the range of possible output values (or dependent variables). By knowing the domain, we can understand where the function is valid and what inputs to consider when analyzing its behavior or graphing it.

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