The powers of a function f: A → A are defined recursively bySuppose ƒ: N → N is defined by...

The powers of a function f: A → A are defined recursively by

Suppose ƒ: N → N is defined by

(a) Prove that ƒ is one-to-one and onto.

(b) [BB] Find the first ten terms of the sequence ƒn(1).

(c) Find the sequence ƒn(2), n ≥ 1.

(d) Find the sequence ƒn(4), n ≥ 1.

(e) Find the first ten terms of the sequence ƒn(8), n ≥ 1.3