Tranformation of the composition

Say: If only oceans were ink for (writing) the words of my Lord, indeed extinguished long before the run out (written) words of my Lord, even if we bring as much addition it (also) QS : alkahfi : 109

There are F and G are Transformation, suppose that:

F: V -> V

G : V -> V

Then the composition of F and G as written G o F defined by

There is a theorem

If F : V -> V

G : V -> V

Then H = G o F : V -> V is transformation.

Those are should surjektif and injektif to proved