Iterated function uses function composition
(f   
  
    
      
        ∘
      
    
    {\displaystyle \circ }
     g)(x) = f (g(x)),always associative.
Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), some mathematicians choose to use ∘ to denote the compositional meaning, writing f∘n(x) for the n-th iterate of the function f(x), as in, for example, f∘3(x) meaning f(f(f(x))). For the same purpose, f [n](x) was used by Benjamin Peirce whereas Alfred Pringsheim and Jules Molk suggested nf(x) instead.