What's the difference between $f \cdot g$ and $f(g(x))$? For example if
$f(x) = x + 2$
and
$g(x) = 4x - 1$
Then what would be the difference in $f \cdot g$ and $f(g(x))$?

If your interpretation of $\cdot$ is $\circ$ as in $f \circ g(x)$ Then,
$f \circ g(x)=f(g(x))$ which is a composite function. Note that $(f \circ g)(x) \neq (g \circ f)(x)$
