1. Let I C R be any interval (open, closed, half-open, bounded or unbounded).If f:I → R is continuous, and for all r, s E Q n I with r

< s we have f(r) < f(s), then for all x < y E I we have f(x) < f(y).(That is show that if f lonI is strictly monotone increasing, then so is f.) 2. Let f : R → R be an exponential function with base a = f(1). Show that f is strictly monotone increasing if a > 1 and strictly monotone decreasing if a < 1.