$f \circ g$
f o g(x)
You mean (f o g)(x) but the thing in the image is actually (g o f)(x) because that's how the composition operator is defined, we first take g and then f and not the other way around.
What are you talking about? OP got it right: https://en.m.wikipedia.org/wiki/Function_composition
God dammit, I always mix it up
to be super pedantic, the right picture should say $x \mapsto f(g(x))$