Answer to Question #290699 in Statistics and Probability for Yaku

Question

a) Consider the following functional relation, f, defined as:

f : R \rightarrow R, f(x) = x2

Determine whether or not f is a bijection. If it is, prove it. If it is not, show why it is not.

b) Consider the set

F = {y | y = ax³ + b},

a, b being constants such that a \ne 0 and x \in R.
Is F equivalent to R? If so, prove it. If not, explain in details why it is not the case.