The domain of a function is the set of all possible input values (or ‘x’ values) for which the function is defined. In the case of the linear function f(x) = 5x + 7, we need to determine the values of x that can be used without leading to any undefined expressions.
For linear functions like this one, there are no restrictions on the values of x. You can plug in any real number, and it will yield a corresponding value of f(x). Therefore, the domain of the function is all real numbers.
In interval notation, we express this as: (−∞, ∞).