Final answer:
The domain of the functions f(x) = x^2 − 1 and g(x) = 2x − 3 is all real numbers which can be denoted as −∞ < x < ∞ as because both quadratic and linear functions are defined for all real values of x.
Step-by-step explanation:
If f(x) = x2 − 1 and g(x) = 2x − 3, the student is asking about the domain of these functions. The domain is the set of all possible input values (x-values) for which the function is defined.
For the function f(x), which is a quadratic function, the domain is all real numbers because there is no restriction on the x-values that we can plug into a quadratic function. This means that any real number squared, minus 1, will result in a real number. Therefore, the domain for f(x) is all real numbers.
The function g(x), which is a linear function, also has a domain of all real numbers. Linear functions do not have restrictions on the values of x that can be used unless explicitly stated. Consequently, for any real number x, 2x − 3 will yield a real number as well.
Therefore, the domain for g(x) is also all real numbers.
In summary, the domain for both f(x) and g(x) is all real numbers, which can be denoted as −∞ < x < ∞.