Let f : R → R , f ( x ) = x^2 ( x −…

Let f : R → R , f ( x ) = x^2 ( x − 3).
(a) Given a real number b , find the number of elements in f
^(-1) [ { b } ]. (The answer will depend on b . It will be helpful
to draw a rough graph of f , and you probably will need ideas from
calculus to complete this exercise.)
(b) Find three intervals whose union is R , such that f is
injective as a function on each interval.
(c) Use your answers to (a) and (b) to define the domain and
codomain of three bijective functions.