We are said to be using left function notation if we write functions to the left of their arguments. That is, if $\alpha : X \to Y$ is a function and $x \in X$ then $\alpha x$ is the image of $x$ under $\alpha$
Furthermore, if we have a function $\beta : Y \to Z$ then we write the composition of the two functions as $\beta \alpha : X \to Z$ and the image of $x$ under the composition as $\beta \alpha x = (\beta \alpha) x = \beta(\alpha x)$
