Consider the following Scala function definitions: def f [X, Y] (a:Option[X], g:X=>Y) : Option[Y] = { a match { case None => None case 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) } } What is the output of running: f (index (List (10, 11, 12), 5), (n:Int) => n * 2)

6. write a user-defined matlab function for the following math function: r() = 4cos(4sin ) the input to the function is  (in radians) and the output is r. write the function such that  can be a vector. a) use the function to calculate r(/6) and r(5/6). b) use the function to plot (polar plot) r() for 0 ≤  ≤ 2. hint: use “ polar” and/or for “polar plot in matlab." include the title “'r(\theta)=4cos(4sin(\theta))”