1. Define f and 9 on R by f(x) = sin x and g(x) = x/lxl if x =f ° and g(O) = 0.

(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.