Answer
$4f(x) + 2f(x) = 2x^2 + 2x + 24$
Domain: all real numbers
Work Step by Step
This exercise asks us to add $2$ times $g(x)$ to $4$ times $f(x)$. Let's write out the problem:
$4f(x) + 2f(x) = 4(2x + 5) + 2(x^2 - 3x + 2)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$4f(x) + 2f(x) = 8x + 20 + 2x^2 - 6x + 4$
Combine like terms:
$4f(x) + 2f(x) = 2x^2 + 2x + 24$
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.
