Final answer:
The domain of f(x) = x - 3 is (-∞, ∞) and the domain of g(x) = (x - 3)/(1 - x) is (-∞, 1)∪(1, ∞). Examples of functions with different domains are provided.
Step-by-step explanation:
The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined. For the function f(x) = x - 3, the domain is all real numbers since there are no restrictions on x.
In interval notation, the domain is (-∞, ∞). For the function g(x) = (x - 3)/(1 - x), the domain is all real numbers except x = 1 because it would result in division by zero. In interval notation, the domain is (-∞, 1)∪(1, ∞).
An example of a function whose domain does not include x = -3 or x = 3 is h(x) = √(x - 2).
The square root function is not defined for negative numbers, so the domain of h(x) is x ≥ 2.
An example of a function with a domain of [-3, 3] is f(x) = x^2, since x^2 is defined for all values of x in that interval.
An example of a function with a domain of (-3, 3) is g(x) = 1/x, where x ≠ 0.
Learn more about Domain of functions