Answer
$g(x) - f(x) = x^2 - x - 12$
$\text{The domain is all real numbers.}$
Work Step by Step
In this problem, we are asked to subtract two functions. Let us go ahead and set up the subtraction problem, separating the two functions with parentheses:
$g(x) - f(x) = (x^2 - 16) - (x - 4)$
Subtract each term of the minuend:
$g(x) - f(x) = x^2 - 16 - x + 4$
Group like terms:
$g(x) - f(x) = x^2 - x - 16 + 4$
Combine like terms:
$g(x) - f(x) = x^2 - x - 12$
The domain is all real numbers since there no values of $x$ that will make the expression above undefined.
