To determine the domain of the function [tex]\( f(x) = x^2 - 6x + 1 \)[/tex], we need to consider the properties and constraints of polynomial functions.
Polynomial functions are expressions that involve variables raised to whole-number exponents and include terms consisting of variables, coefficients, and constants. In general, polynomial functions can take any real number as input without causing any undefined behavior. This is because polynomials are continuous and defined for all real numbers, having no restrictions like division by zero or taking square roots of negative numbers that could limit the domain.
Given that [tex]\( f(x) \)[/tex] is a quadratic polynomial (a polynomial of degree 2), it is defined for all real numbers.
Therefore, the domain of [tex]\( f(x) = x^2 - 6x + 1 \)[/tex] is:
[tex]\[
\boxed{\text{All real numbers}}
\][/tex]
