The powers of a function f: A → A are defined recursively byThe number is known as the go...

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

The number is known as the golden mean. It has many remarkable properties. For instance, the geometric sequence 1, Φ, Φ2, … satisfies the

Fibonacci recurrence relation an+1 = an +an−1 Establish this fact.