How to determine the domain of a rational function

The video tutorial discusses the concept of domain in mathematics, focusing on three functions: f(x) = x^2, f(x) = √x, and f(x) = 1/x. It explains that the domain is the set of all x values that make an equation true. For f(x) = x^2, the domain is all real numbers. For f(x) = √x, the domain is all non-negative numbers. For f(x) = 1/x, the domain is all real numbers except zero. The tutorial also covers solving quadratic equations using methods like factoring and the zero product property.

Explain why the domain of f(x) = 1/x cannot include zero.

What are the values of x that must be excluded from the domain of the function f(x) = (x + 7)(x - 2)?