Let f : X → Y$ and g: Y → Z be functions with the property that the range of f is
a subset of the domain of g. Define a new function g ◦ f : X → Z as follows:
(g ◦ f )(x) = g( f (x)) for all x ∈ X,
where g ◦ f is read “g circle f ” and g( f (x)) is read “g of f of x.” The function g ◦ f
is called the composition of f and g.