Answer
$f(x) + g(x) = x^2 + x - 20$
Domain: all real numbers
Work Step by Step
In this problem, we are asked to add two functions. Let us go ahead and set up the addition problem, separating the two functions with parentheses:
$f(x) + g(x) = (x - 4) + (x^2 - 16)$
Remove the parentheses, but pay attention to the operation in front of the parentheses:
$f(x) + g(x) = x - 4 + x^2 - 16$
Group like terms:
$f(x) + g(x) = x^2 + x - 4 - 16$
Combine like terms:
$f(x) + g(x) = x^2 + x - 20$
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.
