Provide solutions for the following questions. Provide source of your answer and draw graphs where necessary.

18.4 Theorem. Let f be a continuous strictly increasing function on some interval 1. Then f(1) is an interval J by Corollary 18.3 and f-1 represents a function with domain J. The function f-1 is a continuous strictly increasing function on J. Proof The function fis easily shown to be strictly increasing. Since f maps J onto I, the next theorem shows f-1 is continuous. 18.5 Theorem. Let g be a strictly increasing function on an interval J such that g(J) is an interval I. Then g is continuous on J. Proof Consider co in J. We assume To is not an endpoint of J; tiny changes in the proof are needed otherwise. Then g(x0) is not an endpoint of I, so there exists co > 0 such that (g(To) - co, g(x0) + co) CI. Let 0. Since we only need to verify the e-o property of The orem 17.2 for small e, we may assume e