Example 3.5: Again let X = Y = R. Define g by g(x) = x2. The
graph of this function has the familiar parabolic shape as in
Figure 3.1(b). Then for example, g([0, 1]) = [0, 1], g([1,
2]) = [1, 4], g({−1, 1}) = {1}, g−1([0, 1]) = [−1, 1], g−1([1, 2])
= [− √ 2, −1]∪[1, √ 2], g−1([0, ∞)) = R.
*I need help understanding why each example in bold is
the answer it is*
*Please explain...