Answer to Question #294613 in Discrete Mathematics for Yaku

Question

a) Let \mathbb{N} be the set of natural numbers, O, the set of odd numbers and S, the set of

square numbers. Consider the bijections:

f : \mathbb{N} $\to$ O, f(n) = 2n + 1

g : O   S, g(d)=\frac{d2 -2d +1}{4}
Consider f \circ g.

Determine whether or not the specified composition is possible. If it is not possible,

explain in details why it is not. If it is possible, then

i) compute:

1. the resulting composition

2. the corresponding image set

ii) Determine whether or not the specified composition is a bijection.