1. Let f(x) = sin X and g(x) = x/lxl if x =f 0 and g(O) = O.

(a) Find f(E) and g(E) for E = (0,11'), E = [0,11'], E = (-1,1), and E = [-1,1], and explain some of your answers by appealing to results in this section.

(b) Find f-l(E) and g-I(E) for E = (0,1), E = [0,1], E = (-1,1), and E =

[-1,1], and explain some of your answers by appealing to results in this section.