ex_1_45.scm

(define (compose f g) (lambda (x) (f (g x))))

(define (repeated f n)
    (define (iter-repeated i result)
        (if (= i 1)
            result
            (iter-repeated (- i 1) (compose result f))))
    (lambda (x) ((iter-repeated n f) x)))

(define (average a b) (/ (+ a b) 2))

(define (average-damp f)
  (lambda (x) (average x (f x))))

(define tolerance 0.00001)
(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (newline)
      (display guess)
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))

(define (fixed-point-of-transform g transform guess)
  (fixed-point (transform g) guess))

(define (log2 x) (/ (log x) (log 2)))

(define (root n x)
  (fixed-point-of-transform (lambda (y) (/ x (expt y (- n 1))))
                            (repeated average-damp (floor (log2 n)))
                            1.0))