Question

let ( f(x) = 3x + 4 ) and ( g(x) = x^2 - x + 3 ). perform the function operation and then find the domain. ( g(x) - f(x) ) ( g(x) - f(x) = x^2 - 4x - 1 ) (simplify your answer.) what is the domain of ( g(x) - f(x) )? a. the domain of ( g(x) - f(x) ) is the set of all real numbers. b. the domain of ( g(x) - f(x) ) is the set of all ( x geq 0 ). c. the domain of ( g(x) - f(x) ) is the set of all real numbers except ( x = 0 ). d. the domain of ( g(x) - f(x) ) is the set of all ( x leq 0 ).

Explanation:

The function \( g(x) - f(x) = x^2 - 4x - 1 \) is a quadratic function (a polynomial function). Polynomial functions, including quadratics, are defined for all real numbers because there are no restrictions like division by zero or square roots of negative numbers. So the domain is all real numbers.

Answer:

A. The domain of \( g(x) - f(x) \) is the set of all real numbers.