Let f(x) = sin x and g(x) = x/[x] if x 0 and g(0) = 0.

Question:

Let f(x) = sin x and g(x) = x/[x] if x ≠ 0 and g(0) = 0.
a) Find f(£) and g(E) for E = (0, π), E = [0, π], E = (-1, 1), and E = [-1, I]. Compare your answers to what Theorems 10.58, 10.61, and 10.62 predict. Explain any departures from the predictions.
b) Find f-1(E) and g-1(E) for E = (0, 1), E = [0, 1], E = (-1, l), and E = [-1, 1]. Compare your answers to what Theorems 10.58, 10.61, and 10.62 predict. Explain any departures from the predictions.