Define f: R→R by f(x) = x² if x is rational, and f(x) = x if is irrational.
(a) Use the definition to show that limₓ→₀ f(x) = 0. 20 [Hint: 22 < |2], when |2< 1.)
(b) Prove that f is discontinuous at c= -1.
(c) Find all points at which f is continuous. (No proof is needed.)