The domain of a function f (x) is the set of all input values x, for which the function is defined.
For example, for the function
[tex]f(x) = \frac{1}{x-1}[/tex], its domain is all real numbers except the one that makes 0 the denominator of the expression, since the division between 0 is not defined. The value that makes the denominator zero ex x = 1. Then the domain of the function is the set of all real numbers minus the {1}
In this case [tex]f(x) = x (x-9) ^ 2 + 6[/tex], the function f (x), which is a polynomial function, is defined for the set of all real numbers, that is, its domain is all the real numbers.
The range of a function is the set of all possible dependent values that the function can produce. In other words, it is the set of all possible outputs of the function.
For the case of the function [tex]y = x(x-9) ^ 2 + 6[/tex], its range, as well as its domain, covers all real numbers.
