Answer
$(f - g)(x) = -x^2 + 7x + 5$
$\text{Domain: all real numbers}$
Work Step by Step
This exercise asks us to subtract $g(x)$ from $f(x)$. Let's write out the problem:
$(f - g)(x) = f(x) - g(x) = (7x + 5) - (x^2)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$(f - g)(x) = f(x) - g(x) = 7x + 5 - x^2$
Rewrite in a more conventional form in terms of decreasing powers:
$(f - g)(x) = f(x) - g(x) = -x^2 + 7x + 5$
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 $x$ so that we can exclude them from the domain.
In this exercise, $x$ can be any real number, so the domain is all real numbers.
