functional programming - Scala and Writing map functions -

so suppose have function expects set definition int => boolean , function f this:

def map(s: set, f: int => int): set = {}

now how apply f each element of set s.

def map(s: set, f: int => int): set = { (i: int) => f(s(i)) } 

which ofcourse incorrect because in f(s(i)), 's(i)' returns boolean, , can't apply f on it. problem how access each element of set , apply f on it?

this question part of coursera's functional programming scala course.

a goal of course understand functional model, , in case, how set can represented function (called charasteristic function set).

instead of final solution, here's hint on how reason problem:

given characteristic function f: int => boolean defines set , x, int, if f(x) == true, x belongs set. now, if have function g:int=>int want map on set, want apply function elements know belong set: if (f(x)) g(x).

try apply thinking exercise.