Answer
$-2g(x) + f(x) = -2x^2 + 8x + 1$
Domain: all real numbers
Work Step by Step
This exercise asks us to add $f(x)$ to $-2$ times $g(x)$. Let's write out the problem:
$-2g(x) + f(x) = -2(x^2 - 3x + 2) + (2x + 5)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$-2g(x) + f(x) = -2x^2 + 6x - 4 + 2x + 5$
Combine like terms:
$-2g(x) + f(x) = -2x^2 + 8x + 1$
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, so the domain is all real numbers.
