The domain of a function refers to the set of all possible input values (x-values) that the function can accept. In the case of the function f(x) = 5x + 7, we are dealing with a linear function, which is one of the simplest forms of function in mathematics.
For linear functions, there are no restrictions on the values that x can take. This means that x can assume any real number. Thus, the domain of f(x) = 5x + 7 is all real numbers.
We can express the domain in interval notation as:
(−∞, ∞)
In summary, you can choose any real number for x when working with the function f(x) = 5x + 7, and the function will produce a valid output. This characteristic of linear functions is what makes them particularly useful across various applications in mathematics and the real world.