Is there a difference between $(fg)(x)$ and $f(g(x))$? From my lecture slides
$\lim\limits_{x\to a} (f(x)+g(x)) = \lim\limits_{x\to a} f(x) + \lim\limits_{x\to a} g(x)$
Then in the next slide, it shows
$\lim\limits_{x\to a} g(f(x)) = g(\lim\limits_{x\to a} f(x))$
It seem to contradict. Shouldn't it be
$\lim\limits_{x\to a} g(f(x)) = \lim\limits_{x\to a} (gf)(x) = \lim\limits_{x\to a} g(x) \times \lim\limits_{x\to a} f(x)$
Or does $(gf)(x)$ mean $g(x)\cdot f(x)$ not $g(f(x))$? I thought it meant the later.