Question

let $f(x) = 3x + 4$ and $g(x) = x^2 - x + 3$. perform the function operation and then find the domain. $g(x) - f(x)$ $g(x) - f(x) = \square$ (simplify your answer.)

Explanation:

Step1: Substitute the functions

We know that \( f(x) = 3x + 4 \) and \( g(x)=x^{2}-x + 3 \). So we substitute these into \( g(x)-f(x) \):
\( g(x)-f(x)=(x^{2}-x + 3)-(3x + 4) \)

Step2: Distribute the negative sign

Distribute the negative sign to the terms inside the parentheses:
\( x^{2}-x + 3-3x - 4 \)

Step3: Combine like terms

Combine the \( x \)-terms and the constant terms:
For the \( x \)-terms: \( -x-3x=-4x \)
For the constant terms: \( 3 - 4=-1 \)
So we get \( x^{2}-4x - 1 \)

Answer:

\( x^{2}-4x - 1 \)