Classify `f: N->N` given by `f(x)=x^3` as injection, surjection or bijection.

Explanation

Injection condition:

Let `x` and `y` be any two elements in domain `(N)`, such that `f(x) = f(y)`.

`f(x) = f(y)=> x^3 = y^3=> x = y`

So, f is an injection.

Surjection condition:

Let `y` be any element in the co-domain `(N)`, such that `f(x) = y` for some element `x` in `N` (domain).

`f(x) = y=> x^3= y=> x = 3√y` which may not be in `N`.

For example, if `y = 3`, `x = 3√3` is not in `N`.
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