In the textbook I am using to teach mathematics to high school students I found the following illustration about composition of functions.
I do not agree with this illustration. For me $g$ is the slicer, $g(x)$ is the sliced potato, $f$ is the fryer and $f(g(x))$ is the bowl of french fries. I would introduce the notation (not on the diagram though) of $f\circ g$ for the process of slicing and then frying.
Am I being overly pedantic?