Let

Therefore:

Suppose two values of are mapped to the same point (ie. is not injective).

Let and let .

This gives:

Since they are mapped to the same point .

Therefore:

Hence:

From the first (and second rows, i'm cutting some working here) .

From the third row .

We want to cancel out the y's.

.

Therefore:

.

We also have: .

Since we already know that , this implies that .

Hence so the function is injective.