In mathematics, the domain of a function refers to the set of all possible input values (independent variables) for which the function is defined. It is the set of values that you can substitute into a function to get a valid output. The domain is often denoted by the variable x.
For example, consider the function f(x) = 2x + 1. In this case, the domain would typically be all real numbers, as you can plug in any real number for x, and the function will produce a valid result.
However, there are cases where certain values of x might make the function undefined, such as when dividing by zero or taking the square root of a negative number. In such cases, those specific values are excluded from the domain.
It's essential to determine the domain of a function to ensure that you are working with valid input values and to avoid mathematical errors caused by undefined operations.