Iterated Application X55698

Statement

The $n$ -th iterated application of a single-argument function $f$ is the function that, applied to value $x$ , returns $f^n(x)$ , that is, $f(f(...f(x)...))$ , where $f$ is applied $n$ times. Zero applications of $f$ correspond to the identity function (as usual, zero repetitions of anything correspond to a neutral element). Write a function $iterated\_appl(f, n)$ that returns the $n$ -th iterated application of $f$ . The value of $n$ will be a non-negative integer, and $f$ is expected to take floats to floats.

Sample session

>>> iterated_appl(lambda x: x*x, 3)(2)
256.0
>>> sqr = lambda x: x*x
>>> iterated_appl(sqr, 2)(3)
81.0
>>> iterated_appl(sqr, 0)(2)
2.0
>>> add_1 = lambda x: 1+x
>>> iterated_appl(add_1, 5)(3.1)
8.1
>>> iterated_appl(iterated_appl(add_1, 5), 2)(2)
12.0

Information

Author: Jordi Delgado \& José Luis Balcázar
Language: English
Official solutions: Python
User solutions: Python