Prove or give a counterexample for each statement.
(a) If f is continuous on D and k ∈ , then kf is continuous on D.
(b) If f and f + g are continuous on D, then g is continuous on D.
(c) If f and f g are continuous on D, then g is continuous on D.
(d) If f 2 is continuous on D, then f is continuous on D.
(e) If f is continuous on D and D is bounded, then f (D) is bounded.
(f ) If f and g are not continuous on D, then f + g is not continuous on D.
(g) If f and g are not continuous on D, then f g is not continuous on D.
(h) If f : D → E and g : E → F are not continuous on D and E, respectively, then g o f : D → F is not continuous on D.