Define f on [0, ) and g on R by f(x) = x and g(x) = 1/x

Question:

Define f on [0, ∞) and g on R by f(x) = √x and g(x) = 1/x if x ≠ 0 and g(0) = 0.
a) Find f(E) and g(E) for E = (0, 1), E = [0, 1), and E = [0, 1]. Compare your answers with what Theorems 9.26, 9.29, and 9.30 predict. Explain any differences you notice.
b) Find f-l(E) and g-1(E) for E = (-1, 1) and E = [-1, 1]. Compare your answers with what Theorems 9.26, 9.29, and 9.30 predict. Explain any differences you notice.