Answer
$-f(x) + 4g(x) = 4x^2 - 14x + 3$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to add $4$ times $g(x)$ to negative $f(x)$. Let's write out the problem:
$-f(x) + 4g(x) = -(2x + 5) + 4(x^2 - 3x + 2)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$-f(x) + 4g(x) = -2x - 5 + 4x^2 - 12x + 8$
Combine like terms:
$-f(x) + 4g(x) = 4x^2 - 14x + 3$
When we find the domain, we want to find which values of $x$ will cause the function to become undefined; in other words, we want to find any restrictions for $x$. In this exercise, $x$ can be any real number since there are no restrictions, so the domain is all real numbers.
