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

(define (repeated f n)
  (if (> n 1)
      (lambda (x) ((compose (repeated f (- n 1)) f) x))
      f))

(define (n-smooth f n)
  (repeated (smooth f) n)
  )

(define dx 0.00001)

(define (smooth f)
  (lambda (x)
    (/ (+ (f (- x dx)) (f x) (f (+ x dx))) 3)
    )
  )