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.
Derivatives of compositions involving differentiable functions can always be found using the chain rule.
The composition of a function on itself, such as f.f, is customarily written f^{2}. (f.f)(x)=f(f(x))=f^{2}(x). Likewise, (f.f.f)(x)=f(f(f(x)))=f^{3}(x).
In some cases, an expression for f in g(x)=f^{r}(x) can be derived from the rule for g given noninteger values of r. This is called fractional iteration[?].
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