Consider the following Scala function definitions: def f [x,Y] (a:Option(X], g:X=>Y) : Option [T] { = a match f No ne case None cas e Some (x) => Some (g (x)) => def index [X] (xs: List[X], n: Int ) : Option(X) { = xs match case Nil => None case y: : ys if (n == 0) => Some (y) case ys => index (ys, n- 1)