left function notation

We are said to be using 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 functionsas $\beta \alpha :X\to Z$,and the image of $x$ under the compositionas $\beta \alpha x=(\beta \alpha )x=\beta (\alpha x)$.

Compare this to right function notation.