Question

What is the answer to this horrific question my teacher just burst me with in my homework

Answer 1

It's a property of limits:

$\displaystyle\lim_{x\to4}\bigg(g(x)-k(x)\bigg)=\lim_{x\to4}g(x)-\lim_{x\to4}k(x)$

so you end up with 0 - 8, or just -8.