Composite Functions

Let’s consider the following sets:

$$\begin{align*} A &= \{a, b, c, d, e\}\\ B&=\{\alpha , \beta ,\gamma \}\\ C&=\{j, k, l, m, n\}\\ D&=\{u, v, w, x, y, z\}\end{align*}$$

Let’s also consider the functions $f: A\to B, \: g: B\to C,$ and $h:C\to D$, which are defined as follows:

$$\begin{array}{rl}{\displaystyle f}& {\displaystyle =\{(a,\alpha ),(b,\beta ),(c,\gamma ),(d,\alpha ),(e,\beta )\}}\\ {\displaystyle g}& {\displaystyle =\{(\alpha ,j),(\beta ,m),(\gamma ,n)\}}\\ {\displaystyle h}& {\displaystyle =\{(j,z),(k,y),(l,x),(m}\end{array}$$ ...