(a) Show that, for $x \neq -4$, \frac{x^2 - 16}{x + 4} = x - 4.
(b) Are the functions $f(x)$ and $g(x)$ equal?
$f(x) = \frac{x^2 - 16}{x + 4}$, $x \neq -4$
$g(x) = x - 4$, $x \in \mathbb{R}$
The factored form of the numerator is $(x - 4)(x + 4)$.
From the factored form of the numerator, it can be seen that dividing the numerator and denominator by $x + 4$ results in the expression $x - 4$.
(b) Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
(Use a comma to separate answers as needed.)
A. Yes, because $f(x)$ and $g(x)$ have the same values for all values of $x$.
B. No, because on the interval , $f(x) = $ while $g(x) = $
C. No, because on the interval , $f(x) = $ while $g(x)$ is undefined.
D. No, because when $x = $, $g(x) = $ while $f(x)$ is undefined.
E. No, because on the interval , $g(x) = $ while $f(x)$ is undefined.
F. No, because when $x = $, $f(x) = $ while $g(x)$ is undefined.
G. No, because when $x = $, $f(x) = $ while $g(x) = $.
