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

Compare this to left function notation.