1. Let f : (0, 1) R be defined by f(x) = 3 arcsin(x) for all x dom(f). Let g : [/2, /2 ] R be any function with this domain. Define the composite function h = g f on the maximal domain given by these definitions. Finally, define p : dom(h) R by p(x) = h(x)/x for all x dom(h). (a) Determine dom(h). (Note: Do not assign an expression for g(x).) (b) Now suppose that g(x) = sin(x) for all x dom(g). Using only trigonometric identities, determine an algebraic expression for g(3x) in terms of g(x) only. (c) Determine an algebraic expression for h(x). (d) Justify that p has an inverse function p1 by arguing that p is one-to-one. (e) Determine the domain and range of p^1. (f) Determine an algebraic expression for p^1(x).