In the expression
the value of g is the parameter of f, and the function f is composed on g. An equivalent representation is
f.g is a function which is the composite function of f on g.
The composition of a function on itself, such as f.f, is customarily written f2. (f.f)(x)=f(f(x))=f2(x). Likewise, (f.f.f)(x)=f(f(f(x)))=f3(x).
In some cases, an expression for f in g(x)=fr(x) can be derived from the rule for g given non-integer values of r. This is called fractional iteration[?].