A functionf: A-> Ris increasing iff(x)<= f(y)for everyx, y in Asuch thatx<=y.

suppose thatf:[a,b] ->Ris increasing and that for everyY in [f(a), f(b)]there is somex[0] in [a,b]sucht thatf( x[0] ) = Y

How do i show that fis a continious function?