#
Nth repeated application of f
^{
}

If
`f`

is a numerical function and
`n`

is a positive integer, then we can form the
`n`

th repeated application of
`f`

, which is defined to be the function whose value at
`x`

is
`f(f(...(f(x))...))`

. For example, if
`f`

is the function
`x → x + 1`

, then the
`n`

th repeated application of
`f`

is the function
`x → x + n`

. If
`f`

is the operation of squaring a number, then the
`n`

th repeated application of
`f`

is the function that raises its argument to the
`2ⁿ`

th power. Write a procedure that takes as inputs a procedure that computes
`f`

and a positive integer
`n`

and returns the procedure that computes the
`n`

th repeated application of
`f`

. Your procedure should be able to be used as follows:

```
((repeated square 2) 5)
```*625*

Hint: You may find it convenient to use
`compose`

from exercise
1.42
.

```
(define (square x)
(* x x))
(define (inc x)
(+ x 1))
(check-equal? ((repeated square 1) 6) 36)
(check-equal? ((repeated square 2) 5) 625)
(check-equal? ((repeated inc 10) 10) 20)
```