Question

let $f(x)=4x + 5$ and $g(x)=x^2 - x + 2$. perform the function operation and then find the domain.
$g(x)-f(x)$
$g(x)-f(x)=\square$ (simplify your answer.)

Explanation:

Step1: Substitute the functions

$g(x)-f(x)=(x^2 - x + 2)-(4x + 5)$

Step2: Distribute the negative sign

$g(x)-f(x)=x^2 - x + 2 - 4x - 5$

Step3: Combine like terms

$g(x)-f(x)=x^2 + (-x - 4x) + (2 - 5)=x^2 - 5x - 3$

Step4: Determine the domain

The resulting function is a polynomial, which is defined for all real numbers.

Answer:

$g(x)-f(x)=x^2 - 5x - 3$
Domain: All real numbers (or $(-\infty, \infty)$)