Prove or give a counterexample for each statement. a. If f is continuous on D and k ∈ R, 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 fg are continuous on D, then g is continuous on D.
d. If f2 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 fg is not continuous on D.