Assume the following theorem without proof: Theorem. If f is continuous at b and lime-a g(x) = b, then lime-a f(9(x)) = f(b). Using this result, prove the following: Theorem. If g is continuous at a and f is continuous at g(a), then the composition function fog is continuous at a. The following theorem will be accepted without proof. Draw an illustration to explain it. Theorem (Intermediate Value Theorem). Suppose that f is continuous on the closed interval [a, b] and let N be any number between f(a) and f(b) where f(a) # f(b). Then there exists a number c E (a, b) such that f(c) = N