Consider the following Scala function definitions: def f [x,Y] (a:Option(X], g:X= > Y) : Option[T] { = a match case None cas e Some -None => Some (g (x)) (x) def index [X] (xs: List[X], n: Int ) : Option[X] { = xs match case Nil => None case y:ys if (n case yS 0) Some (y -index (ys, n - 1)